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The two observables are complementary if they cannot be measured simultaneously, however they become maximally complementary if their eigenstates are mutually unbiased. Only then the measurement of one observable gives no information about…

Quantum Physics · Physics 2015-05-13 Pawel Kurzynski , Wawrzyniec Kaszub , Mikolaj Czechlewski

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

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d), with d the dimension of the finite Hilbert space, are becoming more and more studied…

Quantum Physics · Physics 2009-11-11 M. Planat , H. C. Rosu

We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free…

Quantum Physics · Physics 2016-01-19 Dardo Goyeneche , Santiago Gomez

Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information theory. In the smallest composite dimension, six, it is known that between three and seven mutually unbiased bases exist, with a decades-old…

Quantum Physics · Physics 2022-08-17 Maria Prat Colomer , Luke Mortimer , Irénée Frérot , Máté Farkas , Antonio Acín

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is constant equal to the inverse $1/\sqrt{d}$, with $d$ the dimension of the finite Hilbert space, are becoming more and…

Quantum Physics · Physics 2009-11-11 Michel Planat , Haret Rosu

In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a…

Quantum Physics · Physics 2025-10-29 Chi-Chuan Hwang

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…

Quantum Physics · Physics 2007-05-23 Somshubhro Bandyopadhyay , P. Oscar Boykin , Vwani Roychowdhury , Farrokh Vatan

If a pure state of a qubit pair is developed over the four basis states, it is known that an equality between the four coefficients of that development exists if and only if that state is unentangled. This paper considers an arbitrary pure…

Quantum Physics · Physics 2019-09-19 Alain Deville , Yannick Deville

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

A collection of orthonormal bases for a complex dXd Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: |<v,w>| ^{2}=1/d. The MUB problem is to…

Quantum Physics · Physics 2007-05-23 Arthur O. Pittenger , Morton H. Rubin

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure…

Quantum Physics · Physics 2018-09-25 Chandan Datta , Satyabrata Adhikari , Arpan Das , Pankaj Agrawal

Ternary quantum systems are being studied because these provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the…

Quantum Physics · Physics 2018-07-06 Ritajit Majumdar , Saikat Basu , Shibashis Ghosh , Susmita Sur-Kolay

In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct…

Mathematical Physics · Physics 2025-08-22 Amit Te'eni , Eliahu Cohen

In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is…

Quantum Physics · Physics 2009-11-13 A. J. Skinner , V. A. Newell , R. Sanchez

Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of…

Quantum Physics · Physics 2019-03-04 Thomas Durt , Berthold-Georg Englert , Ingemar Bengtsson , Karol Życzkowski

The study of Mutually Unbiased Bases continues to be developed vigorously, and presents several challenges in the Quantum Information Theory. Two orthonormal bases in $\mathbb C^d, B {and} B'$ are said mutually unbiased if $\forall b\in B,…

Quantum Physics · Physics 2009-08-12 M. Combescure

A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and…

Quantum Physics · Physics 2011-02-10 Stephen Brierley , Stefan Weigert

In quantum information, complementarity of quantum mechanical observables plays a key role. If a system resides in an eigenstate of an observable, the probability distribution for the values of a complementary observable is flat. The…

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…

Quantum Physics · Physics 2015-06-23 U. Seyfarth , L. L. Sanchez-Soto , G. Leuchs