Physik in unserer Zeit
50
(6)
269-270
(2019)
| Journal
Vor rund zwei Jahrzehnten gelang erstmals die Quantenteleportation, also die Übertragung von Quanteninformation mit Hilfe der Verschränkung. Unserer Gruppe am Institute for Quantum Optics and Quantum Information (IQOQI) Vienna ist es nun in Kooperation mit einem chinesischen Team gelungen, dreidimensionale Zustände von Photonen zu übertragen.
Quantum Teleportation in High Dimensions
Yi-Han Luo,
Han-Sen Zhong,
Manuel Erhard,
Xi-Lin Wang,
Li-Chao Peng,
Mario Krenn,
Xiao Jiang,
Li Li,
Nai-Le Liu, et al.
Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.
Questions on the Structure of Perfect Matchings Inspired by Quantum Physics
Mario Krenn,
Xuemei Gu,
Daniel Soltesz
Proceedings of the 2nd Croatian Combinatorial Days
(2019)
| Journal
| PDF
We state a number of related questions on the structure of perfect matchings. Those questions are inspired by and directly connected to Quantum Physics. In particular, they concern the constructability of general quantum states using modern photonic technology. For that we introduce a new concept, denoted as inherited vertex coloring. It is a vertex coloring for every perfect matching. The colors are inherited from the color of the incident edge for each perfect matching.<br>First, we formulate the concepts and questions in pure graph-theoretical language, and finally we explain the physical context of every mathematical object that we use. Importantly, every progress towards answering these questions can directly be translated into new understanding in quantum physics.
Quantum experiments and graphs. III. High-dimensional and multiparticle
entanglement
Xuemei Gu,
Lijun Chen,
Anton Zeilinger,
Mario Krenn
Physical Review A
99
(3)
032338
(2019)
| Journal
| PDF
Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.
Quantum experiments and graphs II: Quantum interference, computation,
and state generation
Xuemei Gu,
Manuel Erhard,
Anton Zeilinger,
Mario Krenn
Proceedings of the National Academy of Sciences of the United States of America
116
(10)
4147-4155
(2019)
| Journal
We present an approach to describe state-of-the-art photonic quantum experiments using graph theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. This viewpoint immediately leads to many interesting results, some of which we present here. First, we identify an experimental unexplored multiphoton interference phenomenon. Second, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Third, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights into quantum state generation with current photonic technology. Fourth, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and graph theory offers another perspective on a widely used technology and immediately raises many follow-up questions.
Arbitrary d-dimensional Pauli X gates of a flying qudit
Xiaoqin Gao,
Mario Krenn,
Jaroslav Kysela,
Anton Zeilinger
Physical Review A
99
(2)
023825
(2019)
| Journal
| PDF
High-dimensional degrees of freedom of photons can encode more quantum information than their two-dimensional counterparts. While the increased information capacity has advantages in quantum applications (such as quantum communication), controlling and manipulating these systems has been challenging. Here we show a method to perform deterministic arbitrary high-dimensional Pauli X gates for single photons carrying orbital angular momentum. The X gate consists of a cyclic permutation of qudit basis vectors and, together with the Z gate, forms the basis for performing arbitrary transformations. The proposed experimental setups only use two basic optical elements such as mode sorters and mode shifters and thus could be implemented in any system where these experimental tools are available. Furthermore the number of involved interferometers scales logarithmically with the dimension, which is important for practical implementation.
Contact
Prof. Mario Krenn
University of Tübingen Maria-von-Lindenstrasse 6 72076 Tübingen, Germany
