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The connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article we classify MUBs according to their degree of covariance with…

Mathematical Physics · Physics 2016-06-23 Claudio Carmeli , Jussi Schultz , Alessandro Toigo

Mutually unbiased bases plays a central role in quantum mechanics and quantum information processing. As an important class of mutually unbiased bases, mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have attracted…

Information Theory · Computer Science 2020-01-01 Dengming Xu

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration…

Mathematical Physics · Physics 2007-05-23 Metod Saniga , Michel Planat

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

Analysis of state reconstruction both classical and quantum mechanical on equal footing is outlined. The meaning of "mutual unbiased bases" (MUB) of Hilbert spaces is explained in detail. An alternative quantum state reconstruction, that…

Quantum Physics · Physics 2009-12-31 M. Revzen

In this contribution we group the operator basis for d^2 dimensional Hilbert space in a way that enables us to relate bases of entangled states with single particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize…

Quantum Physics · Physics 2015-05-13 A. Kalev , F. C. Khanna , M. Revzen

We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard…

Combinatorics · Mathematics 2012-01-04 Mate Matolcsi , Imre Z. Ruzsa , Mihaly Weiner

We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…

Quantum Physics · Physics 2008-05-19 Gary McConnell , David Gross

The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the…

Quantum Physics · Physics 2011-03-31 T. Paterek , M. Pawlowski , M. Grassl , C. Brukner

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 has various application in quantum information procession and coding theory. There can be maximum d + 1 MUBs in C^d and d/2 +1 MUBs in R^d. But , over R^d MUBs are known to be non existent when d is odd and for most…

Quantum Physics · Physics 2025-12-16 Ajeet Kumar , Uditanshu Sadual

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

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 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

We construct an informationally complete set of mutually unbiased - like bases for N ququarts. These bases are used in an explicit tomographic protocol which performance is analyzed by estimating quadratic errors and compared to other…

Quantum Physics · Physics 2021-08-10 Juan Díaz-Guevara , Isabel Sainz , Andrei B. Klimov

The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing…

Quantum Physics · Physics 2023-01-18 Taiyu Zhang , Lin Chen

A complete set of mutually unbiased bases in a Hilbert space of dimension $d$ defines a set of $d+1$ orthogonal measurements. Relative to such a set, we define a "MUB-balanced state" to be a pure state for which the list of probabilities of…

Quantum Physics · Physics 2015-06-22 Ilya Amburg , Roshan Sharma , Daniel Sussman , William K. Wootters

The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained…

Quantum Physics · Physics 2009-09-11 Maurice Robert Kibler

We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras…

Quantum Algebra · Mathematics 2025-04-29 Sooyeong Kim , David Kribs , Edison Lozano , Rajesh Pereira , Sarah Plosker