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Related papers: Mutually Unbiased Bases for Continuous Variables

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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

Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUB) for the space of operators, $M(d, \mathbb{C})$, acting on such Hilbert spaces. The notion of MUUB reflects the…

Quantum Physics · Physics 2020-12-21 Rinie N. M. Nasir , Jesni Shamsul Shaari , Stefano Mancini

Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing a complete set for optimal quantum state tomography. In this work, we investigate the detection of entanglement via…

Quantum Physics · Physics 2021-09-14 B. C. Hiesmayr , D. McNulty , S. Baek , S. Singha Roy , J. Bae , D. Chruściński

There has been great interest in finding sets of $m$ mutually unbiased bases which are compatible with a given space $\mathbb{C}^d$, specially in physics due to their interesting applications in quantum information theory. Several general…

Quantum Physics · Physics 2014-01-08 J. Batle

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate…

Quantum Physics · Physics 2018-01-25 Daniel S. Tasca , Piero Sánchez , Stephen P. Walborn , Łukasz Rudnicki

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

Relative and center of mass cordinates are used to generalize mutually unbiased bases (MUB) and define mutually unbiased bases (MUCB). Maximal entangled states are given as product staes in the collective varibles

Quantum Physics · Physics 2015-05-14 M. Revzen

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

We consider questions posed in a recent paper of Mandayam, Bandyopadhyay, Grassl and Wootters [10] on the nature of "unextendible mutually unbiased bases." We describe a conceptual framework to study these questions, using a connection…

Quantum Physics · Physics 2014-07-11 Koen Thas

Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the…

Quantum Physics · Physics 2009-09-25 Julia Evans , Ross Duncan , Alex Lang , Prakash Panangaden

In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be…

Quantum Physics · Physics 2025-12-18 Seyed Javad Akhtarshenas , Saman Karimi , Mahdi Salehi

Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is…

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

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

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 have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of $N$ MUBs. Our result is valid…

Quantum Physics · Physics 2021-08-18 Bilal Canturk , Zafer Gedik

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 (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with…

Combinatorics · Mathematics 2012-06-05 Joanne L. Hall , Jan Stovicek

We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…

Quantum Physics · Physics 2023-08-04 Luke Mortimer

One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon is most strongly manifested when observables are related to mutually unbiased bases. In this paper, we…

Quantum Physics · Physics 2015-05-27 M. Wiesniak , T. Paterek , A. Zeilinger

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