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Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain…

Discrete Mathematics · Computer Science 2025-07-04 Arindam Banerjee , Kanoy Kumar Das , Ajeet Kumar , Rakesh Kumar , Subhamoy Maitra

We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB-projectors) as input states for a D-dimensional quantum system, with D being a power of a prime number. This approach connects the results of…

Quantum Physics · Physics 2015-05-27 A. Fernández-Pérez , A. B. Klimov , C. Saavedra

The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single…

Quantum Physics · Physics 2009-11-13 Stefan Weigert , Michael Wilkinson

A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension, $d$, of the considered Hilbert space is a power of…

Quantum Physics · Physics 2013-11-27 Christoph Spengler , Barbara Kraus

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

Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…

Quantum Physics · Physics 2015-06-12 A. B. Klimov , G. Bjork , L. L. Sanchez-Soto

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by: i) introducing families…

Quantum Physics · Physics 2021-02-12 Armin Tavakoli , Máté Farkas , Denis Rosset , Jean-Daniel Bancal , Jędrzej Kaniewski

This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an…

Quantum Physics · Physics 2015-06-26 Metod Saniga , Michel Planat

In this paper, we consider the problem of Mutually Unbiased Bases in prime dimension $d$. It is known to provide exactly $d+1$ mutually unbiased bases. We revisit this problem using a class of circulant $d \times d$ matrices. The…

Mathematical Physics · Physics 2007-10-31 M. Combescure

We employ a straightforward relation between mutually unbiased and Bell bases to extend the latter in terms of a direct construction for the former. We analyze in detail the properties of these new generalized Bell states, showing that they…

Quantum Physics · Physics 2009-10-23 A. B. Klimov , D. Sych , L. L. Sanchez-Soto , G. Leuchs

A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1 MUBs. We…

Quantum Physics · Physics 2013-05-29 Jay Lawrence

We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are…

Quantum Physics · Physics 2011-09-02 Wim van Dam , Alexander Russell

The notation of mutually unbiased bases(MUB) was first introduced by Ivanovic to reconstruct density matrixes\cite{Ivanovic}. The subject about how to use MUB to analyze, process, and utilize the information of the second moments between…

Information Theory · Computer Science 2007-12-19 Hongyi Yao

We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…

Quantum Physics · Physics 2009-11-11 Ulrike Herzog , Janos A. Bergou

We present a detailed computational and algebraic study of Mutually Unbiased Bases (MUBs) in finite-dimensional Hilbert spaces, with a particular focus on dimensions 2, 3, 4, and the challenging case of 6. Starting from the Hadamard-phase…

Quantum Physics · Physics 2026-04-03 Jean-Christophe Pain

Inspired by the many applications of mutually unbiased Hadamard matrices, we study mutually unbiased weighing matrices. These matrices are studied for small orders and weights in both the real and complex setting. Our results make use of…

Combinatorics · Mathematics 2013-08-01 Darcy Best , Hadi Kharaghani , Hugh Ramp

Excluding the existence of four MUBs in $\bbC^6$ is an open problem in quantum information. We investigate the number of product vectors in the set of four mutually unbiased bases (MUBs) in dimension six, by assuming that the set exists and…

Quantum Physics · Physics 2018-07-13 Lin Chen , Li Yu

In a quantum system having a finite number $N$ of orthogonal states, two orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept appears in…

Quantum Physics · Physics 2007-05-23 Claude archer

We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the squares of the moduli of their scalar products are equal to zero, one, or 1/d. These sets will be called a MU constellation, and…

Quantum Physics · Physics 2008-10-21 Stephen Brierley , Stefan Weigert

Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if |<b|b'>|^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of…

Quantum Physics · Physics 2023-11-27 Andreas Klappenecker , Martin Roetteler