We establish the multiparameter quantum Cramér-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, the Cramér-Rao bound is independent of the source separation, which confirms that the Rayleigh resolution limit is just an artifact of the<br>conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can<br>gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost important in realistic scenarios, such as observational astronomy.
Quantum metrology at the limit with extremal Majorana constellations
F. Bouchard,
P. de la Hoz,
G. Bjork,
R. W. Boyd,
Markus Grassl,
Z. Hradil,
E. Karimi,
A. B. Klimov,
Gerd Leuchs, et al.
Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation<br>constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings of Quantumness are especially germane for this task<br>when the rotation axis is unknown, as they have a sensitivity independent of that axis and they achieve a Heisenberg-limit scaling. Here, we report the<br>experimental realization of these states by generating up to 21-dimensional orbital angular momentum states of single photons, and confirm their high metrological abilities.<br>
Fibonacci-Lucas SIC-POVMs
Markus Grassl,
Andrew J. Scott
Journal of Mathematical Physics
58
122201
(2017)
| Preprint
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| PDF
We present a conjectured family of SIC-POVMs which have an additional
symmetry group whose size is growing with the dimension. The symmetry group is
related to Fibonacci numbers, while the dimension is related to Lucas numbers.
The conjecture is supported by exact solutions for dimensions
d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.
Unraveling beam self-healing
Andrea Aiello,
Girish S. Agarwal,
Martin Paur,
Bohumil Stoklasa,
Zdenek Hradil,
Jaroslav Rehacek,
Pablo de la Hoz,
Gerd Leuchs,
Luis L. Sanchez-Soto
Optics Express
25
(16)
19147-19157
(2017)
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| PDF
We show that, contrary to popular belief, diffraction-free beams not only may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field. (C) 2017 Optical Society of America
Efficient tomography with unknown detectors
L. Motka,
M. Paur,
J. Rehacek,
Z. Hradil,
L. L. Sanchez-Soto
We compare the two main techniques used for estimating the state of a
physical system from unknown measurements: standard detector tomography and
data-pattern tomography. Adopting linear inversion as a fair benchmark, we show
that the difference between these two protocols can be traced back to the
nonexistence of the reverse-order law for pseudoinverses. We capitalize on this
fact to identify regimes where the data-pattern approach outperforms the
standard one and vice versa. We corroborate these conclusions with numerical
simulations of relevant examples of quantum state tomography.
Invariant tensors are states in the SU(2) tensor product representation that are invariant under the SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly<br>entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors recently has attracted a lot of<br>attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is a $n$-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPT. For bivalent tensors, the invariant perfect tensor is the unique singlet state for each local dimension. The trivalent invariant perfect tensor also exists and is uniquely given by Wigner's 3j symbol. However, we show that, surprisingly, there does not exist four-valent invariant perfect tensors for any dimension. On the contrary, when the dimension is large, almost all invariant tensors are perfect asymptotically, which is a consequence of the phenomenon of<br>concentration of measure for multipartite quantum states.
Towards optimal quantum tomography with unbalanced homodyning
Yong Siah Teo,
Hyunseok Jeong,
Luis L. Sanchez-Soto
Balanced homodyning, heterodyning and unbalanced homodyning are the three
well-known sampling techniques used in quantum optics to characterize all
possible photonic sources in continuous-variable quantum information theory. We
show that for all quantum states and all observable-parameter tomography
schemes, which includes the reconstructions of arbitrary operator moments and
phase-space quasi-distributions, localized sampling with unbalanced homodyning
is always tomographically more powerful (gives more accurate estimators) than
delocalized sampling with heterodyning. The latter is recently known to often
give more accurate parameter reconstructions than conventional marginalized
sampling with balanced homodyning. This result also holds for realistic
photodetectors with subunit efficiency. With examples from first- through
fourth-moment tomography, we demonstrate that unbalanced homodyning can
outperform balanced homodyning when heterodyning fails to do so. This new
benchmark takes us one step towards optimal continuous-variable tomography with
conventional photodetectors and minimal experimental components.
Focusing characteristics of a 4 pi parabolic mirror light-matter interface
Lucas Alber,
Martin Fischer,
Marianne Bader,
Klaus Mantel,
Markus Sondermann,
Gerd Leuchs
JOURNAL OF THE EUROPEAN OPTICAL SOCIETY-RAPID PUBLICATIONS
13
14
(2017)
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| PDF
Background: Focusing with a 4 pi parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality.
Methods: To determine these errors, we experimentally examine the focusing properties of a 4p parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single Yb-174(+) ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap.
Results: We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface.
Conclusion: Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4p parabolic mirror.
Coarse graining the phase space of N qubits
Olivia Di Matteo,
Luis Sanchez-Soto,
Gerd Leuchs,
Markus Grassl
We develop a systematic coarse graining procedure for systems of N qubits. We exploit the underlying geometrical structures of the associated discrete<br>phase space to produce a coarse-grained version with reduced effective size. Our coarse-grained spaces inherit key properties of the original ones. In<br>particular, our procedure naturally yields a subset of the original measurement operators, which can be used to construct a coarse discrete Wigner function. These operators also constitute a systematic choice of incomplete measurements for the tomographer wishing to probe an intractably large system.
Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of<br>the other. We investigate small sets of complementary observables that cannot be extended by yet another complementary observable. We construct explicit<br>examples of the unextendible sets up to dimension $16$ and conjecture certain small sets to be unextendible in higher dimensions. Our constructions provide<br>three complementary measurements, only one observable away from the ultimate minimum of two observables in the set. Almost all of our examples in finite dimension allow to discriminate pure states from some mixed states, and shed light on the complex topology of the Bloch space of higher-dimensional quantum systems.<br>
Shifting the phase of a coherent beam with a Yb-174(+) ion: influence of the scattering cross section
Martin Fischer,
Bharath Srivathsan,
Lucas Alber,
Markus Weber,
Markus Sondermann,
Gerd Leuchs
APPLIED PHYSICS B-LASERS AND OPTICS
123
(1)
48
(2017)
| Journal
| PDF
We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an Yb-174(+) ion. In the derivation of the expected phase shifts, we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling (Hensch and Schawlow in Opt Commun 13:68-69,1975).
Generic method for lossless generation of arbitrarily shaped photons
We put forward a generic method that enables lossless generation of pure single photons with arbitrary shape over any degree of freedom or several degrees of freedom simultaneously. The method exploits pairs of entangled photons. One of the photons is the subject for lossy shaping manipulations followed by a specially designed mode-equalizing measurement. A successful measurement outcome heralds the losslessly shaped second photon. The method has three crucial ingredients that define the quantum state of the shaped photon: the initial bipartite state of the photons, modulation of the first photon, and its mode-equalizing detection. We provide a specific recipe with a combination of these ingredients for achieving any desired pure state of the shaped photon.
Experimental detection of entanglement polytopes via local filters
Yuan-Yuan Zhao,
Markus Grassl,
Bei Zeng,
Guo-Yong Xiang,
Chao Zhang,
Chuan-Feng Li,
Guang-Can Guo
Quantum entanglement, resulting in correlations between subsystems that are stronger than any possible classical correlation, is one of the mysteries of quantum mechanics. Entanglement cannot be increased by any local operation, and for a sufficiently large many-body quantum system there exist infinitely many different entanglement classes, i. e., states that are not related by stochastic local operations and classical communications. On the other hand, the method of entanglement polytopes results in finitely many coarse-grained types of entanglement that can be detected by only measuring single-particle spectra. We find, however, that with high probability the local spectra lie in more than one polytope, hence providing only partial information about the entanglement type. To overcome this problem, we propose to additionally use so-called local filters, which are non-unitary local operations. We experimentally demonstrate the detection of entanglement polytopes in a four-qubit system. Using local filters we can distinguish the entanglement type of states with the same single particle spectra, but which belong to different polytopes.
Fundamental precision limit of a Mach-Zehnder interferometric sensor
when one of the inputs is the vacuum
Masahiro Takeoka,
Kaushik P. Seshadreesan,
Chenglong You,
Shuro Izumi,
Jonathan P. Dowling
In the lore of quantum metrology, one often hears (or reads) the following no-go theorem: If you put a vacuum into one input port of a balanced Mach-Zehnder interferometer, then no matter what you put into the other input port, and nomatter what your detection scheme, the sensitivity can never be better than the shot-noise limit (SNL). Often the proof of this theorem is cited to be inC. Caves, Phys. Rev. D23, 1693 (1981), but upon further inspection, no such claim is made there. Quantum-Fisher-information-based arguments suggestive of this no-go theorem appear elsewhere in the literature, but are not stated in their full generality. Here we thoroughly explore this no-go theorem and give a rigorous statement: the no-go theorem holds whenever the unknown phase shift is split between both of the arms of the interferometer, but remarkably does not hold when only one arm has the unknown phase shift. In the latter scenario, we provide an explicit measurement strategy that beats the SNL. We also point out that these two scenarios are physically different and correspond to different types of sensing applications.
Complementarity and Polarization Modulation in Photon Interference
Andreas Norrman,
Kasimir Blomstedt,
Tero Setala,
Ari T. Friberg
We derive two general complementarity relations for the distinguishability and visibility of genuine vector-light quantum fields in double-pinhole photon interference involving polarization modulation. The established framework reveals an intrinsic aspect of wave-particle duality of the photon, not previously reported, thus providing deeper insights into foundational quantum interference physics.
Plasmon coherence determination by nanoscattering
Yahong Chen,
Andreas Norrman,
Sergey A. Ponomarenko,
Ari T. Friberg
We present a simple and robust protocol to recover the second-order field correlations of polychromatic, statistically stationary surface plasmon polaritons (SPPs) from a spectrum measurement in the far zone of a dipolar nanoscatterer. The recovered correlations carry comprehensive information about the spectral, spatial, and temporal coherence of the SPPs. We also introduce and exemplify for the first time, to the best of our knowledge, the two-point Stokes parameters associated with partially coherent SPP fields. (C) 2017 Optical Society of America
Extracting the physical sector of quantum states
D. Mogilevtsev,
Y. S. Teo,
J. Rehacek,
Z. Hradil,
J. Tiedau,
R. Kruse,
G. Harder,
C. Silberhorn,
L. L. Sanchez-Soto
The physical nature of any quantum source guarantees the existence of an effective Hilbert space of finite dimension, the physical sector, in which its state is completely characterized with arbitrarily high accuracy. The extraction of this sector is essential for state tomography. We show that the physical sector of a state, defined in some pre-chosen basis, can be systematically retrieved with a procedure using only data collected from a set of commuting quantum measurement outcomes, with no other assumptions about the source. We demonstrate the versatility and efficiency of the physical-sector extraction by applying it to simulated and experimental data for quantum light sources, as well as quantum systems of finite dimensions.
Some results on the structure of constacyclic codes and new linear codes over GF(7) from quasi-twisted codes
Nuh Aydin,
Nicholas Connolly,
Markus Grassl
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
11
(1)
245-258
(2017)
| Journal
One of the most important and challenging problems in coding theory is to construct codes with good parameters. There are various methods to construct codes with the best possible parameters. A promising and fruitful approach has been to focus on the class of quasi-twisted (QT) codes which includes constacyclic codes as a special case. This class of codes is known to contain many codes with good parameters. Although constacyclic codes and QT codes have been the subject of numerous studies and computer searches over the last few decades, we have been able to discover a new fundamental result about the structure of constacyclic codes which was instrumental in our comprehensive search method for new QT codes over GF(7). We have been able to find 41 QT codes with better parameters than the previously best known linear codes. Furthermore, we derived a number of additional new codes via Construction X as well as standard constructions, such as shortening and puncturing.
Lempel-Ziv Complexity of Photonic Quasicrystals
Juan J. Monzon,
Angel Felipe,
Luis L. Sanchez-Soto
The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. Here, we assess the quasicrystal structural features in terms of the Lempel-Ziv complexity. This is an easily calculable quantity that has proven to be useful for describing patterns in a variety of systems. One feature of great practical relevance is that it provides a reliable measure of how hard it is to create the structure. Using the generalized Fibonacci quasicrystals as our thread, we give analytical fitting formulas for the dependence of the optical response with the complexity.
Optimally cloned binary coherent states
C. R. Mueller,
G. Leuchs,
Ch. Marquardt,
U. L. Andersen
Binary coherent state alphabets can be represented in a two-dimensional Hilbert space. We capitalize this formal connection between the otherwise distinct domains of qubits and continuous variable states to map binary phase-shift keyed coherent states onto the Bloch sphere and to derive their quantum-optimal clones. We analyze the Wigner function and the cumulants of the clones, and we conclude that optimal cloning of binary coherent states requires a nonlinearity above second order. We propose several practical and near-optimal cloning schemes and compare their cloning fidelity to the optimal cloner.
Free-space quantum links under diverse weather conditions
D. Vasylyev,
A. A. Semenov,
W. Vogel,
K. Guenthner,
A. Thurn,
O. Bayraktar,
Ch. Marquardt
Free-space optical communication links are promising channels for establishing secure quantum communication. Here we study the transmission of nonclassical light through a turbulent atmospheric link under diverse weather conditions, including rain or haze. To include these effects, the theory of light transmission through atmospheric links in the elliptic-beam approximation presented by Vasylyev et al. [D. Vasylyev et al., Phys. Rev. Lett. 117, 090501 (2016)] is further generalized. It is demonstrated, with good agreement between theory and experiment, that low-intensity rain merely contributes additional deterministic losses, whereas haze also introduces additional beam deformations of the transmitted light. Based on these results, we study theoretically the transmission of quadrature squeezing and Gaussian entanglement under these weather conditions.
High-dimensional intracity quantum cryptography with structured photons
Alicia Sit,
Frederic Bouchard,
Robert Fickler,
Jeremie Gagnon-Bischoff,
Hugo Larocque,
Khabat Heshami,
Dominique Elser,
Christian Peuntinger,
Kevin Guenthner, et al.
Quantum key distribution (QKD) promises information-theoretically secure communication and is already on the verge of commercialization. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate. Hitherto, no experimental verification of high-dimensional QKD in the singlephoton regime has been conducted outside of the laboratory. Here, we report the realization of such a single-photon QKD system in a turbulent free-space link of 0.3 km over the city of Ottawa, taking advantage of both the spin and orbital angular momentum photonic degrees of freedom. This combination of optical angular momenta allows us to create a 4-dimensional quantum state; wherein, using a high-dimensional BB84 protocol, a quantum bit error rate of 11% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. In comparison, an error rate of 5% with a secret key rate of 0.43 bits per sifted photon is achieved for the case of 2-dimensional structured photons. We thus demonstrate that, even through moderate turbulence without active wavefront correction, high-dimensional photon states are advantageous for securely transmitting more information. This opens the way for intracity high-dimensional quantum communications under realistic conditions. (C) 2017 Optical Society of America
Free-space propagation of high-dimensional structured optical fields in
an urban environment
Martin P. J. Lavery,
Christian Peuntinger,
Kevin Guenthner,
Peter Banzer,
Dominique Elser,
Robert W. Boyd,
Miles J. Padgett,
Christoph Marquardt,
Gerd Leuchs
Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantum-state tomography. We present experimental data for the modal degradation in a real urban environment and draw a comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in an urban environment.
Quantum-limited measurements of optical signals from a geostationary
satellite
Kevin Guenthner,
Imran Khan,
Dominique Elser,
Birgit Stiller,
Oemer Bayraktar,
Christian R. Mueller,
Karen Saucke,
Daniel Troendle,
Frank Heine, et al.
The measurement of quantum signals that travel through long distances is fundamentally and technologically interesting. We present quantum-limited coherent measurements of optical signals that are sent from a satellite in geostationary Earth orbit to an optical ground station. We bound the excess noise that the quantum states could have acquired after having propagated 38,600 km through Earth's gravitational potential, as well as its turbulent atmosphere. Our results indicate that quantum communication is feasible, in principle, in such a scenario, highlighting the possibility of a global quantum key distribution network for secure communication. (C) 2017 Optical Society of America
Quantum communication with coherent states of light
Imran Khan,
Dominique Elser,
Thomas Dirmeier,
Christoph Marquardt,
Gerd Leuchs
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL
AND ENGINEERING SCIENCES
375
(2099)
20160235
(2017)
| Journal
Quantum communication offers long-term security especially, but not only, relevant to government and industrial users. It is worth noting that, for the first time in the history of cryptographic encoding, we are currently in the situation that secure communication can be based on the fundamental laws of physics ( information theoretical security) rather than on algorithmic security relying on the complexity of algorithms, which is periodically endangered as standard computer technology advances. On a fundamental level, the security of quantum key distribution (QKD) relies on the non-orthogonality of the quantum states used. So even coherent states are well suited for this task, the quantum states that largely describe the light generated by laser systems. Depending on whether one uses detectors resolving single or multiple photon states or detectors measuring the field quadratures, one speaks of, respectively, a discrete- or a continuous-variable description. Continuous-variable QKD with coherent states uses a technology that is very similar to the one employed in classical coherent communication systems, the backbone of today's Internet connections. Here, we review recent developments in this field in two connected regimes: (i) improving QKD equipment by implementing front-end telecom devices and (ii) research into satellite QKD for bridging long distances by building upon existing optical satellite links.
This article is part of the themed issue 'Quantum technology for the 21st century'.
Temporal and spectral properties of quantum light
B. Stiller,
U. Seyfarth,
G. Leuchs,
C. Fabre,
V. Sandoghdar,
N. Treps,
L.F. Cugliandolo
Quantum Optics and Nanophotonics
169-227
(2017)
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| PDF
Orbital angular momentum modes of high-gain parametric down-conversion
Lina Beltran,
Gaetano Frascella,
Angela M. Perez,
Robert Fickler,
Polina R. Sharapova,
Mathieu Manceau,
Olga V. Tikhonova,
Robert W. Boyd,
Gerd Leuchs, et al.
Light beams with orbital angular momentum (OAM) are convenient carriers of quantum information. They can. also be. used for imparting rotational motion to particles and providing. high resolution in imaging. Due to the conservation of OAM in parametric down-conversion (PDC), signal and idler photons generated at low gain have perfectly anti-correlated OAM values. It is interesting to study the OAM properties of high-gain PDC, where the same OAM modes can be populated with large, but correlated, numbers of photons. Here we investigate the OAM spectrum of high-gain PDC and show that the OAM mode content can be controlled by varying the pump power and the configuration of the source. In our experiment, we use a source consisting of two nonlinear crystals separated by an air gap. We discuss the OAM properties of PDC radiation emitted by this source and suggest possible modifications.
New self-dual additive F_4-codes constructed from circulant graphs
In order to construct quantum [[n, 0, d]] codes for (n, d) = (56, 15), (57, 15), (58, 16), (63, 16), (67, 17), (70, 18), (71, 18), (79, 19), (83, 20), (87, 20), (89, 21), (95, 20), we construct self-dual additive F-4-codes of length n and minimum weight d from circulant graphs. The quantum codes with these parameters are constructed for the first time. (C) 2016 Elsevier B.V. All rights reserved.
Optimal measurements for resolution beyond the Rayleigh limit
J. Rehacek,
M. Paur,
B. Stoklasa,
Z. Hradil,
L. L. Sanchez-Soto
We establish the conditions to attain the ultimate resolution predicted by quantum estimation theory for the case of two incoherent point sources using a linear imaging system. The solution is closely related to the spatial symmetries of the detection scheme. In particular, for real symmetric point spread functions, any complete set of projections with definite parity achieves the goal. (C) 2017 Optical Society of America
Improving the phase super-sensitivity of squeezing-assisted
interferometers by squeeze factor unbalancing
The sensitivity properties of an SU(1,1) interferometer made of two cascaded parametric amplifiers, as well as of an ordinary SU(2) interferometer preceded by a squeezer and followed by an anti-squeezer, are theoretically investigated. Several possible experimental configurations are considered, such as the absence or presence of a seed beam, direct or homodyne detection scheme. In all cases we formulate the optimal conditions to achieve phase super-sensitivity, meaning a sensitivity overcoming the shotnoise limit. Weshow that for a given gain of the first parametric amplifier, unbalancing the interferometer by increasing the gain of the second amplifier improves the interferometer properties. In particular, a broader super-sensitivity phase range and a better overall sensitivity can be achieved by gain unbalancing.
Discrete phase-space structures and Wigner functions for N qubits
C. Munoz,
A. B. Klimov,
L. Sanchez-Soto
QUANTUM INFORMATION PROCESSING
16
(6)
UNSP 158
(2017)
| Journal
We further elaborate on a phase-space picture for a system of N qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and different entanglement properties. We discuss the construction of discrete covariant Wigner functions for these bundles and provide several illuminating examples.
Roadmap on structured light
Halina Rubinsztein-Dunlop,
Andrew Forbes,
M. V. Berry,
M. R. Dennis,
David L. Andrews,
Masud Mansuripur,
Cornelia Denz,
Christina Alpmann,
Peter Banzer, et al.
Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.
Multiphoton Effects Enhanced due to Ultrafast Photon-Number Fluctuations
Kirill Yu. Spasibko,
Denis A. Kopylov,
Victor L. Krutyanskiy,
Tatiana V. Murzina,
Gerd Leuchs,
Maria V. Chekhova
The rate of an n-photon effect generally scales as the nth order autocorrelation function of the incident light, which is high for light with strong photon-number fluctuations. Therefore, "noisy" light sources are much more efficient for multiphoton effects than coherent sources with the same mean power, pulse duration, and repetition rate. Here we generate optical harmonics of the order of 2-4 from a bright squeezed vacuum, a state of light consisting of only quantum noise with no coherent component. We observe up to 2 orders of magnitude enhancement in the generation of optical harmonics due to ultrafast photon-number fluctuations. This feature is especially important for the nonlinear optics of fragile structures, where the use of a noisy pump can considerably increase the effect without overcoming the damage threshold.
Experimental demonstration of negative-valued polarization
quasiprobability distribution
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for position and momentum. Most notably, they both give correct one-dimensional marginal probability distributions and therefore represent the natural choice for the probability distributions in classical hidden-variable models. In this context, negativity of the Wigner function is considered as proof of nonclassicality for a quantum state. On the contrary, the polarization quasiprobability distribution demonstrates negativity for all quantum states. This feature comes from the discrete nature of Stokes variables; however, it was not observed in previous experiments, because they were performed with photon-number averaging detectors. Here we reconstruct the polarization quasiprobability distribution of a coherent state with photon-number resolving detectors, which allows us to directly observe for the first time its negativity. Furthermore we derive a theoretical polarization quasiprobability distribution for any linearly polarized quantum state.
Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer
Mathieu Manceau,
Gerd Leuchs,
Farid Khalili,
Maria Chekhova
In an unseeded SU(1,1) interferometer composed of two cascaded degenerate parametric amplifiers, with direct detection at the output, we demonstrate a phase sensitivity overcoming the shot noise limit by 2.3 dB. The interferometer is strongly unbalanced, with the parametric gain of the second amplifier exceeding the gain of the first one by a factor of 2, which makes the scheme extremely tolerant to detection losses. We show that by increasing the gain of the second amplifier, the phase supersensitivity of the interferometer can be preserved even with detection losses as high as 80%. This finding can considerably improve the state-of-the-art interferometry, enable sub-shot-noise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.
Dimensionality of random light fields
Andreas Norrman,
Ari T. Friberg,
Jose J. Gil,
Tero Setala
JOURNAL OF THE EUROPEAN OPTICAL SOCIETY-RAPID PUBLICATIONS
13
36
(2017)
| Journal
Background: The spectral polarization state and dimensionality of random light are important concepts in modern optical physics and photonics.
Methods: By use of space-frequency domain coherence theory, we establish a rigorous classification for the electricfield vector to oscillate in one, two, or three spatial dimensions.
Results: We also introduce a new measure, the polarimetric dimension, to quantify the dimensional character of light. The formalism is utilized to show that polarized three-dimensional light does not exist, while an evanescent wave generated in total internal reflection generally is a genuine three-dimensional light field.
Conclusions: The framework we construct advances the polarization theory of random light and it could be beneficial for near-field optics and polarization-sensitive applications involving complex-structured light fields.
Free space excitation of coupled Anderson-localized modes in photonic
crystal waveguides with polarization tailored beam
Ali Mahdavi,
Paul Roth,
Jolly Xavier,
Taofiq K. Paraiso,
Peter Banzer,
Frank Vollmer
We experimentally demonstrate free space excitation of coupled Anderson-localized modes in photonic crystal (PhC) line-defect waveguides (W1) with polarization tailored beams. The corresponding light beam is tightly focused on a pristine W1, and out-of-plane scattering is imaged. By integrating the scattering spectra along the guide, at the W1 modal cut-off, Anderson-localized cavities are observed due to residual W1 fabrication-disorder. Their spectral lines exhibit high quality Q factors up to 2 x 10(5). The incident beam polarization and scattering intensities of the localized modes characterize the efficiency of free-space coupling. The coupling is studied for linearly and radially polarized input beams and for different input coupling locations along the W1 guide. The proposed coupling scheme is particularly attractive for excitation of PhC waveguide modes and Anderson-localized cavities by beam steering and scanning microscopy for sensing applications. Published by AIP Publishing.
Superiority of heterodyning over homodyning: An assessment with
quadrature moments
Y. S. Teo,
C. R. Mueller,
H. Jeong,
Z. Hradil,
J. Rehacek,
L. L. Sanchez-Soto
We examine the moment-reconstruction performance of both the homodyne and heterodyne (doublehomodyne) measurement schemes for arbitrary quantum states and introduce moment estimators that optimize the respective schemes for any given data. In the large-data limit, these estimators are as efficient as the maximum-likelihood estimators. We then illustrate the superiority of the heterodyne measurement for the reconstruction of the first and second moments by analyzing Gaussian states and many other significant nonclassical states. Finally, we present an extension of our theories to two-mode sources, which can be straightforwardly generalized to all other multimode sources.
Progress toward optimal quantum tomography with unbalanced homodyning
Balanced homodyning, heterodyning, and unbalanced homodyning are three well-known sampling techniques used in quantum optics to characterize photonic sources in the continuous-variable regime. We show that for all quantum states and all observable-parameter tomography schemes, which includes reconstructions of arbitrary operator moments and phase-space quasidistributions, localized sampling with unbalanced homodyning is always tomographically more powerful (gives more accurate estimators) than delocalized sampling with heterodyning. The latter is recently known to often give more accurate parameter reconstructions than conventional marginalized sampling with balanced homodyning. This result also holds for realistic photodetectors with subunit efficiency. With examples from first-through fourth-moment tomography, we demonstrate that unbalanced homodyning can outperform balanced homodyning when heterodyning fails to do so. This new benchmark takes us one step towards optimal continuous-variable tomography with conventional photodetectors and minimal experimental components.
Linear and angular momenta in tightly focused vortex segmented beams of light
Martin Neugebauer,
Andrea Aiello,
Peter Banzer
Chinese Optics Letters
15
(3)
030003
(2017)
| Journal
| PDF
We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.
Polarization-Selective Out-Coupling of Whispering-Gallery Modes
Florian Sedlmeir,
Matthew R. Foreman,
Ulrich Vogl,
Richard Zeltner,
Gerhard Schunk,
Dmitry V. Strekalov,
Christoph Marquardt,
Gerd Leuchs,
Harald G. L. Schwefel
Whispering-gallery mode (WGM) resonators are an important platform for linear, nonlinear, and quantum optical experiments. In such experiments, independent control of in-coupling and out-coupling rates to different modes can lead to higher conversion efficiencies and greater flexibility in the generation of nonclassical states based on parametric down-conversion. In this work, we introduce a scheme that enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and the coupler such that a negative (positive) birefringence allows for polarization-selective coupling to TE (TM) WGMs. We formulate a refined coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive a criterion for polarization-selective coupling. Finally, we experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a 22-dB suppression of coupling to TM modes relative to TE modes.
Temporal shaping of single photons enabled by entanglement
Valentin Averchenko,
Denis Sych,
Gerhard Schunk,
Ulrich Vogl,
Christoph Marquardt,
Gerd Leuchs
We present a method to produce pure single photons with an arbitrary designed temporal shape in a heralded way. As an indispensable resource, the method uses pairs of time-energy entangled photons. One photon of a pair undergoes temporal amplitude-phase modulation according to the desired shape. Subsequent frequency-resolved detection of the modulated photon heralds its entangled counterpart in a pure quantum state. The temporal shape of the heralded photon is indirectly affected by the modulation in the heralding arm. We derive conditions for which the shape of the heralded photon is given by the modulation function. The method can be implemented with various sources of time-energy entangled photons. In particular, using entangled photons from parametric down-conversion the method provides a simple means to generate pure shaped photons with an unprecedented broad range of temporal durations, from tenths of femtoseconds to microseconds. This shaping of single photons will push forward the implementation of scalable multidimensional quantum information protocols, efficient photon-matter coupling, and quantum control at the level of single quanta.
Characterization and shaping of the time-frequency Schmidt mode spectrum
of bright twin beams generated in gas-filled hollow-core photonic
crystal fibers
M. A. Finger,
N. Y. Joly,
P. St. J. Russell,
M. V. Chekhova
We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagome-style photonic crystal fiber by adjusting the pressure, pump pulse chirp, fiber length, and parametric gain. Compared to solid-core systems, the pressure-dependent dispersion landscape brings increased flexibility to the tailoring of frequency correlations, and we demonstrate that the pump pulse chirp can be used to tune the joint spectrum of femtosecond-pumped.(3) sources. We also characterize the resulting mode content, not only by measuring the multimode second-order correlation function g((2)), but also by directly reconstructing the shapes and weights of time-frequency Schmidt (TFS) modes. We show that the number of modes directly influences the shot-to-shot pulse-energy and spectral-shape fluctuations in MI. Using this approach we control and monitor the number of TFS modes within the range from 1.3 to 4 using only a single fiber.
Unconstrained Capacities of Quantum Key Distribution and Entanglement
Distillation for Pure-Loss Bosonic Broadcast Channels
Masahiro Takeoka,
Kaushik P. Seshadreesan,
Mark M. Wilde
We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We show a simple example of a broadcast QKD protocol overcoming the limit of the point-to-point strategy. Our result is thus an important step toward opening a new framework of network channel-based quantum communication technology.
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