Related papers: Mutually equibiased bases
We discuss what can be inferred from measurements on one- and two-qubit systems using a single measurement basis at various times. We show that, given reasonable physical assumptions, carrying out such measurements at quarter-period…
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…
The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the…
When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…
Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…
Unextendible sets of Mutually Unbiased Bases (MUBs) are examined from the point of view of complementary subalgebras. We show, that the linear span of less than $d+1$ factors of $M_d \otimes M_d$ does not contain pure states, and therefore…
The task of measuring in two mutually unbiased bases is central to many quantum information protocols, as well as being of fundamental interest. Increasingly, there is an experimental focus on generating and controlling high-dimensional…
We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we…
We introduce the notion of the unextendible maximally entangled basis (UMEB), a set of orthonormal maximally entangled states in d \times d consisting of fewer that d^2 vectors which have no additional maximally entangled vectors orthogonal…
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…
Entanglement, a critical resource for quantum information processing, needs to be witnessed in many practical scenarios. Theoretically, witnessing entanglement is by measuring a special Hermitian observable, called entanglement witness…
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…
We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables…
Distilling high-dimensional quantum entanglement under realistic, general asymmetric noise remains a formidable challenge. Standard entanglement purification protocols inevitably fail to satisfy convergence constraints under severe…
We introduce a new state discrimination problem in which we are given additional information about the state after the measurement, or more generally, after a quantum memory bound applies. In particular, the following special case plays an…
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…
We derive a novel version of information-disturbance theorems for mutually unbiased observables. We show that the information gain by Eve inevitably makes the outcomes by Bob in the conjugate basis not only erroneous but random.
Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of…