Related papers: Detecting Entanglement can be More Effective with …
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
The resource theoretic measure of quantum coherence is basis dependent, and the amount of coherence contained in a state is different in different bases. We obtained analytical solutions for the maximum coherence by optimizing the reference…
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…
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how…
We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased…
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…
Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum…
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…
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…
Entanglement, while being critical in many quantum applications, is difficult to characterize experimentally. While entanglement witnesses based on the fidelity to the target entangled state are efficient detectors of entanglement, they in…
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
In this paper, we explore the concept of Mutually Unbiased Bases (MUBs) in discrete quantum systems. It is known that for dimensions $d$ that are powers of prime numbers, there exists a set of up to $d+1$ bases that form an MUB set.…
We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of simple feasibility problems, which provides sufficient conditions to entanglement. Our…
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…
An unextendible biseparable basis (UBB) is a set of orthogonal pure biseparable states which span a subspace of a given Hilbert space while the complementary subspace contains only genuinely entangled states. These biseparable bases are…
Certifying entanglement for unknown quantum states experimentally is a fundamental problem in quantum computing and quantum physics. Because of being easy to implement, a most popular approach for this problem in modern quantum experiments…
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension