Article
Multidisciplinary Sciences
Armin Tavakoli, Mate Farkas, Denis Rosset, Jean-Daniel Bancal, Jedrzej Kaniewski
Summary: The text discusses the importance of mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) in quantum theory, particularly in the context of quantum nonlocality. It highlights the development of Bell inequalities, device-independent certification, and protocols for quantum key distribution and quantum random number generation using MUBs and SICs. Additionally, it presents the first example of an extremal point in the quantum set of correlations with physically inequivalent quantum realizations.
Article
Physics, Multidisciplinary
Yajuan Zang, Zihong Tian, Hui-Juan Zuo, Shao-Ming Fei
Summary: Based on maximally entangled states, this paper explores the constructions of mutually unbiased bases in bipartite quantum systems. A new way to construct mutually unbiased bases using difference matrices in the theory of combinatorial designs is presented. Various constructions of mutually unbiased bases are established, including cases involving prime power q and composite numbers of non-prime power d.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Quantum Science & Technology
Tian Xie, Yajuan Zang, Hui-Juan Zuo, Shao-Ming Fei
Summary: We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Examples in specific cases demonstrate the advantages of our approach.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Physics, Multidisciplinary
Bilal Canturk, Zafer Gedik
Summary: The paper investigates the optimal upper bound of entropic uncertainty relation for N Mutually Unbiased Bases (MUBs) and provides a quantitative criterion for the extendibility of MUBs based on entropic certainty relation. The results are also applied to the information exclusion relation of (d+1) observables conditioned with a classical memory to detect the compatibility of the observables.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Quantum Science & Technology
Xiaoyu Chen, Mengfan Liang, Mengyao Hu, Lin Chen
Summary: The research shows that if there are four MUBs, then the H-2-reducible matrix within them contains exactly nine 2x2 Hadamard submatrices. This result has been utilized to exclude some known CHMs from the four MUBs. These findings represent the latest progress on the existence of six-dimensional MUBs.
QUANTUM INFORMATION PROCESSING
(2021)
Article
Optics
Gelo Noel M. Tabia, Varun Satya Raj Bavana, Shih-Xian Yang, Yeong-Cherng Liang
Summary: This article examines the problem of exhibiting Bell nonlocality for a two-qudit entangled pure state using a randomly chosen set of mutually unbiased bases (MUBs). The research finds that even with only two-setting Bell inequalities, there is a significant chance of obtaining a Bell violation if the two parties are individually allowed to measure a sufficient number of MUBs.
Article
Quantum Science & Technology
Lai-Zhen Luo, Yu Xia, Gui-Jun Zhang
Summary: We study mutually unbiased maximally entangled bases (MUMEBs) in bipartite system C-d⨂C-d with d >= 3, where d is a power of an odd prime number. By utilizing the theory of finite fields, we present a novel and intuitive method for constructing MUMEBs in C-d⨂C-d. Specifically, we construct d(d - 1) MUMEBs in the bipartite system C-d⨂C-d explicitly.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Physics, Multidisciplinary
Liu Sun, Yuan-Hong Tao, Lin Song Li
Summary: This paper focuses on the Tsallis relative 2-entropy of coherence of quantum states under mutually unbiased bases (MUBs) in two, three, and four-dimensional systems. The study reveals that for single-qubit mixed states, the sum under complete MUBs is less than v6; for Gisin states and Bell-diagonal states in the four-dimensional system, the sum under a new set of autotensor of mutually unbiased basis (AMUBs) is less than nine. It is also found that for three classes of X states in the three-dimensional system, each Tsallis relative 2-entropy of coherence under nontrivial unbiased bases is equal. Additionally, the surfaces of the sum of the Tsallis relative 2-entropy of coherence under MUBs and AMUBs are described, with a special class of X states in AMUBs forming an ellipsoid.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2023)
Article
Quantum Science & Technology
Zehong Chang, Yunlong Wang, Zhenyu Guo, Min An, Rui Qu, Junliang Jia, Fumin Wang, Pei Zhang
Summary: The transverse spatial mode of light plays a crucial role in high-dimensional quantum key distribution (QKD). However, practical applications face challenges such as mode-dependent loss and system complexity, which hinder achieving higher dimensions, longer distances, and lower costs in communications. To address these issues, a mutually partially unbiased bases (MPUBs) protocol has been proposed, which fundamentally eliminates the effects of mode-dependent loss for long propagation distances and limited aperture sizes. In this study, we successfully implemented the MPUBs protocol in dimensions of 2, 4, 5, and 6. By employing a controlled unitary transformation, we were able to actively switch the measurement basis and create a compact measurement system. As a result, we achieved higher encoding dimensions using finite system resources, leading to higher key rates and stronger noise resistance. Our work enhances the practicality of the MPUBs protocol and contributes to the advancement of high-dimensional QKD in quantum networks.
QUANTUM SCIENCE AND TECHNOLOGY
(2023)
Article
Optics
Yao Zhou, Zhen-Qiang Yin, Shuang Wang, Wei Chen, Guang-Can Guo, Zheng-Fu Han
Summary: In this paper, we propose a method to improve the key rate at long distances and the maximum achievable distance for twin-field quantum key distribution (TF-QKD) by deriving the error rates under three mutually unbiased bases in two-dimensional Hilbert space. By learning these error rates, noisy preprocessing can be added to further enhance the performance. We also find that higher bit error rates do not necessarily result in lower key rates when noisy preprocessing is employed. Our method only requires simple postprocessing of experimental data without changing the existing physical implementation or experimental operation, leading to notable enhancements in key rate and maximum achievable distance for the phase-encoded TF-QKD protocol, as demonstrated by simulation results.
Article
Quantum Science & Technology
Yi-Hao Sheng, Jian Zhang, Yuan-Hong Tao, Shao-Ming Fei
Summary: The study focuses on the complementarity and uncertainty relations of coherence under mutually unbiased bases using skew information. It also derives the complementarity relation for geometric measure of coherence based on the coherence via skew information. As applications, two tighter upper bounds are presented for minimum error probabilities in discriminating a set of pure states with least square measurement, improving upon previous results.
QUANTUM INFORMATION PROCESSING
(2021)
Article
Physics, Multidisciplinary
Yuan-Hong Tao, Xin-Lei Yong, Yi-Fan Han, Shu-Hui Wu, Cai-Hong Wang
Summary: The research focuses on mutually unbiased bases formed by special entangled basis with fixed Schmidt number 2, establishing a systematic way of construction and proposing a general approach from different contexts. Detailed examples in various environments are provided, and limitations from previous studies are successfully eliminated.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
B. C. Hiesmayr, D. McNulty, S. Baek, S. Singha Roy, J. Bae, D. Chruscinski
Summary: In this study, the detection of entanglement using inequivalent sets of MUBs, including unextendible MUBs, was explored, showing that such sets can be more effective in entanglement verification. An efficient method to search for inequivalent MUBs was provided, with a regular occurrence of such sets within the Heisenberg-Weyl MUBs as dimension increases. The findings suggest that a clever selection of MUBs can lead to entanglement detection with fewer measurements, which is particularly useful for experimentalists.
NEW JOURNAL OF PHYSICS
(2021)
Article
Quantum Science & Technology
Yinhong Cao
Summary: This article introduces a novel quantum protocol for quantum secure multi-party geometry computation, which provides unconditional security for Euclidean distance computation and can withstand various attacks.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Physics, Multidisciplinary
Evgeny Zelenov
Summary: This paper investigates the representation of Weyl commutation relations using coherent states over a field of p-adic numbers. A lattice in a vector space over the p-adic field corresponds to a family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and the operators defining the quantization of symplectic dynamics are Hadamard operators.
Article
Multidisciplinary Sciences
Peter Adam, Vladimir A. Andreev, Margarita A. Man'ko, Vladimir I. Man'ko, Matyas Mechler
Summary: The article explores the construction of an invertible map from density operators to functions through quantizers and dequantizers, focusing on examples of qubit and qutrit states. It also delves into the study of biphoton states in the probability representation of quantum mechanics during parametric down-conversion.
Article
Physics, Multidisciplinary
Sergio De Nicola, Renato Fedele, Dusan Jovanovic, Margarita A. Man'ko, Vladimir I. Man'ko
Summary: The study explores the tomography of a single quantum particle in an accelerated frame, demonstrating the existence of a Gaussian wave packet solution unaffected by acceleration. The application of Radon transform helps determine the quantum tomogram of the Gaussian state evolution in the accelerated frame.
Article
Physics, Multidisciplinary
Olga V. Man'ko, Vladimir I. Man'ko
Summary: This review discusses the new formulation of conventional quantum mechanics where quantum states are regarded as probability distributions, and an invertible map of density operators and wave functions onto probability distributions is constructed. Examples of probability representations of qubits, harmonic oscillators, and free particles are studied in detail, and equations for the evolution of quantum systems are written in the form of linear classical-like equations for probability distributions. Relations to phase-space representation of quantum states and classical mechanics are also elucidated.
Article
Physics, Multidisciplinary
Julio A. Lopez-Saldivar, Margarita A. Man'ko, Vladimir Man'ko
Summary: The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems are obtained using the covariance matrix. The proposal to define a temperature scale for these states using the area of the Wigner function and the width of the tomogram is confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. These properties are mentioned as measures for the temperature of quantum systems.
Article
Physics, Multidisciplinary
Yury Belousov, Vladimir I. Man'ko, Agostino Migliore, Alessandro Sergi, Antonino Messina
Summary: This study investigates a system of two spins 1/2, revealing the notable symmetry properties of the corresponding Hamiltonian model and showing the characteristics of S-2. By appropriate mapping, it is possible to simulate the time evolution of a pseudo-qutrit, and investigate the dynamic similitude using two types of representation for the initial density matrix of the two spins.
Article
Optics
Andrey Yu Fedorov, Vladimir Man'ko
Summary: This passage discusses the superposition principle of a qubit, formulating it as a nonlinear addition rule of the mean values of spin projections onto three perpendicular directions. It also provides explicit expressions for the mean values that determine the superposition states, based on the mean values of two initial pure states of the qubit.
JOURNAL OF RUSSIAN LASER RESEARCH
(2022)
Article
Physics, Multidisciplinary
Sergey Filippov
Summary: Researchers have developed a tensor network formalism to address the challenges in standard collision models, namely, describing quantum correlations among ancillas induced by successive system-ancilla interactions, and dealing with initially correlated ancillas. They found that matrix product state (matrix product density operator) is effective in capturing induced correlations in the standard collision model if the colliding particles are in pure (mixed) states. Additionally, they constructed a general tensor diagram for system dynamics and derived a memory-kernel master equation to handle initially correlated ancillas, considering multipoint correlations beyond two-point correlations.
Article
Physics, Multidisciplinary
Vladimir N. Chernega, Olga Man'ko, Vladimir Man'ko
Summary: This paper discusses the application of superposition states of two qubits and entangled Bell states in the probability representation of quantum mechanics. It formulates the superposition principle using the nonlinear addition rule of state density matrices and explores the extension of entanglement properties to the case of superposition of two-mode oscillator states using the probability representation of quantum states.
Article
Physics, Multidisciplinary
Julio A. Lopez-Saldivar, Margarita A. Man'ko, Vladimir I. Man'ko
Summary: In the framework of probability representation in quantum mechanics, we investigated a superposition of Gaussian states associated with the symmetries of a regular polygon. By obtaining the Wigner functions and tomographic probability distributions, we explicitly determined the density matrices of these states as sums of Gaussian terms. The obtained results exhibit nonclassical behavior and varied extrema for each state, with the number of critical points reflecting the order of the symmetry group defining the states.
Article
Physics, Multidisciplinary
Sergey Filippov, Alena Termanova
Summary: In the realm of continuous-variable states and local Gaussian channels, the assumption that the optimal initial state with the most robust entanglement is Gaussian is proven to be false. Specific non-Gaussian two-mode states are shown to remain entangled under the effect of deterministic local attenuation or amplification. These results challenge the Gaussian world paradigm in quantum information science.
Article
Physics, Multidisciplinary
I. A. Luchnikov, E. O. Kiktenko, M. A. Gavreev, H. Ouerdane, S. N. Filippov, A. K. Fedorov
Summary: The article introduces a data-driven approach to analyzing the non-Markovian dynamics of open quantum systems, which can capture key characteristics of the system and reconstruct predictive models while denoising measured data.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Optics
Yu M. Belousov, N. N. Elkin, V. Man'ko, S. Revenko, I. A. Tarakanov, L. N. Tikhomirova
Summary: The tomographic representation for signal processing is applied in the study of living system signals. The use of a reference signal allows for the observation of tomogram transformations for functions described by f(t) and f(-t). The results show that this approach provides new opportunities for obtaining additional and useful information.
JOURNAL OF RUSSIAN LASER RESEARCH
(2022)
Article
Optics
Sergey N. Filippov
Summary: This study considers polarization-dependent losses and proposes physically motivated multipartite entangled states that outperform factorized states, which is significant for improving quantum communication rates.
Article
Optics
Sergey N. Filippov, Ilia A. Luchnikov
Summary: This paper presents an exact solution to the interaction problem between a quantum system and individual particles or modes using the tensor network formalism. The solution addresses the challenges posed by classical and quantum environment correlations, advancing the application of tensor-network methods in quantum optics and quantum transport.
Article
Optics
Peter Adam, Margarita A. Man'ko, Vladimir Man'ko
Summary: This article discusses even and odd coherent states in quantum mechanics and their probability representation. The formalism of quantizer and dequantizer operators is used to construct Wigner functions, and the relationship between Wigner functions and probability distributions is obtained through the Radon integral transform. The concept of entangled classical probability distributions is introduced in probability theory.
JOURNAL OF RUSSIAN LASER RESEARCH
(2022)
