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Related papers: On mutually unbiased bases

200 papers

We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables…

Quantum Physics · Physics 2021-10-08 Stan Gudder

We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a…

Quantum Physics · Physics 2009-11-13 Shengjun Wu , Sixia Yu , Klaus Mølmer

We construct general schemes for multi-partite quantum secret sharing using multi-level systems, and find that the consistent conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using the very…

Quantum Physics · Physics 2015-07-22 I-Ching Yu , Feng-Li Lin , Ching-Yu Huang

A long-standing open problem asks if there can exist 7 mutually unbiased bases (MUBs) in $\mathbb{C}^6$, or, more generally, $d + 1$ MUBs in $\mathbb{C}^d$ for any $d$ that is not a prime power. The recent work of Kolountzakis, Matolcsi,…

Optimization and Control · Mathematics 2022-03-01 Afonso S. Bandeira , Nikolaus Doppelbauer , Dmitriy Kunisky

We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic description of a SIC-POVM in dimension six is…

Quantum Physics · Physics 2009-05-25 Markus Grassl

Quantum measurements based on mutually unbiased bases (MUB) play crucial roles in foundational studies and quantum information processing. It is known that there exist inequivalent MUB, but little is known about their operational…

Quantum Physics · Physics 2023-11-14 Wen-Zhe Yan , Yunting Li , Zhibo Hou , Huangjun Zhu , Guo-Yong Xiang , Chuan-Feng Li , Guang-Can Guo

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is…

Combinatorics · Mathematics 2015-05-27 W. K. Kantor

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation,…

Quantum Physics · Physics 2017-12-04 Feiran Wang , Manuel Erhard , Amin Babazadeh , Mehul Malik , Mario Krenn , Anton Zeilinger

All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive…

Quantum Physics · Physics 2012-03-27 Daniel McNulty , Stefan Weigert

We study the connection between mutually unbiased bases and mutually orthogonal extraordinary supersquares, a wider class of squares which does not contain only the Latin squares. We show that there are four types of complete sets of…

Quantum Physics · Physics 2014-04-24 Iulia Ghiu , Cristian Ghiu

Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…

Quantum Physics · Physics 2017-09-07 Lu Liu , Ting Gao , Fengli Yan

Mutually unbiased bases (MUB) are useful in a number of research areas. The symmetry of MUB is an elusive and interesting subject. A (complete set of) MUB in dimension $d$ is sharply covariant if it can be generated by a group of order…

Quantum Physics · Physics 2015-09-09 Huangjun Zhu

A simple recipe for generating a complete set of mutually unbiased bases in dimension (2j+1)**e, with 2j + 1 prime and e positive integer, is developed from a single matrix acting on a space of constant angular momentum j and defined in…

Quantum Physics · Physics 2007-05-23 M. R. Kibler , M. Planat

We consider particular entanglement of two particles whose state vectors are in bases that are mutually unbiased (MUB), i.e. "that exhibit maximum degree of incompatibility" (J.Schwinger,Nat. Ac. Sci. (USA), 1960)). We use this link between…

Quantum Physics · Physics 2008-09-12 M. Revzen , F. C. Khanna

From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to…

Quantum Physics · Physics 2023-03-14 Joonwoo Bae , Anindita Bera , Dariusz Chruściński , Beatrix C. Hiesmayr , Daniel McNulty

Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…

Quantum Physics · Physics 2015-11-11 J. Rehacek , Z. Hradil , Y. S. Teo , L. L. Sanchez-Soto , H. K. Ng , J. H. Chai , B. -G. Englert

Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and…

Quantum Physics · Physics 2018-02-27 Lu Liu , Ting Gao , Fengli Yan

We examine the existence and structure of particular sets of mutually unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known power-of-prime MUB constructions, we restrict ourselves to using maximally entangled…

Quantum Physics · Physics 2011-09-02 Wim van Dam , Mark Howard

The resource theoretic measure of quantum coherence is basis dependent, and the amount of coherence contained in a state is different in different bases. We obtained analytical solutions for the maximum coherence by optimizing the reference…

Quantum Physics · Physics 2017-11-13 Ming-Liang Hu , Shu-Qian Shen , Heng Fan

Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…

Quantum Physics · Physics 2024-05-31 Nadish de Silva , Ming Yin , Sergii Strelchuk