Related papers: Mutually Unbiased Bases in Composite Dimensions --…
Inspired by the many applications of mutually unbiased Hadamard matrices, we study mutually unbiased weighing matrices. These matrices are studied for small orders and weights in both the real and complex setting. Our results make use of…
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…
Previous studies on the geometrical properties of the state space of a finite-level quantum system have determined its volume and surface area. Building on this foundation, we derive explicit formulas for two additional intrinsic volume…
An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional…
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…
Unextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. Their comprehensive characterization is thus of great importance and has been a subject of vital…
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…
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…
I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than two bases. These, I call the nUB conditions, and the corresponding bases $n$-fold unbiased. They naturally appear while optimizing generic…
Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and…
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 give a synthetic construction of a complete system of mutually unbiased bases in $\mathbb{C}^3$.
In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased…
We show how to transform the problem of finding d+1 mutually unbiased bases in the d-dimensional Hilbert space into the one of finding d(d+1) vectors in the N-dimensional Hilbert space with N=d**2. The transformation formulas admit a…
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…
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…
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…
We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the…
Quantum systems with variables in ${\mathbb Z}(d)$ are considered. The properties of lines in the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space of these systems, are studied. Weak mutually unbiased bases in these systems are defined as…
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…