Related papers: Geometrical approach to mutually unbiased bases
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…
An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of…
In this contribution we relate two different key concepts: mutually unbiased bases (MUBs) and entanglement; in particular we focus on bound entanglement, i.e. highly mixed states which cannot be distilled by local operations and classical…
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…
Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of…
We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in $C^2 \otimes C^4$. Based on this condition, an…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting…
We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find…
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…
We present two complementary approaches to the GKSL equation for an open qubit. The first, based on linearity, yields solutions illustrated by mixed states trajectories in the Bloch ball, including non-random asymptotic fixed points, and…
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…
Mutually unbiased bases (MUB) are an elusive discrete structure in Hilbert spaces. Many (complete sets of) MUB are group covariant, but little is known whether they can be sharply covariant in the sense that the generating groups can have…
We investigate the $l_{1}$ norm of coherence of quantum states in mutually unbiased bases. We find that the sum of squared $l_{1}$ norm of coherence of the mixed state single qubit is less than two. We derive the $l_{1}$ norm of coherence…
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…
We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and…
A set of mutually unbiased bases (MUBs) is said to be unextendible if there does not exist another basis that is unbiased with respect to the given set. Here, we prove the existence of smaller sets of MUBs in prime-squared dimensions…
We present a construction method for complete sets of cyclic mutually unbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. In comparison to usual complete sets of MUBs, complete cyclic sets possess the additional property…
We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond…
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…
Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane.