Related papers: Measures to characterise Approximate Mutually Unbi…
We prove a Tb theorem on quasimetric spaces equipped with what we call an upper doubling measure. This is a property that encompasses both the doubling measures and those satisfying the upper power bound \mu(B(x,r)) \le Cr^d. Our spaces are…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
We exhibit an operational connection between mutually unbiased bases and symmetric infomationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures…
Garnett, Killip, and Schul have exhibited a doubling measure $\mu$ with support equal to $\mathbb{R}^{d}$ which is $1$-rectifiable, meaning there are countably many curves $\Gamma_{i}$ of finite length for which…
We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $d+1$ MUMs on any density operator $\rho$ in…
The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…
We study unextendible maximally entangled bases (UMEBs) in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d'$). An operational method to construct UMEBs containing $d(d^{\prime}-1)$ maximally entangled vectors is established, and…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
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 introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon is most strongly manifested when observables are related to mutually unbiased bases. In this paper, we…
Finite geometry is used to underpin finite, two d-dimensional particles Hilbert space, d=prime 6= 2. A central role is allotted to states with mutual unbiased bases (MUB) labeling. Dual affine plane geometry (DAPG) points underpin single…
Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a…
We study the connection between mutually unbiased bases and mutually orthogonal extraordinary supersquares, a wider class of squares which does not contain only the Latin squares. We show that there are four types of complete sets of…
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…
We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical…
In this paper, we prove that the existence of a complete set of mutually unbiased bases (MUBs) in N-dimensional Hilbert space implies the existence of a complete set of mutually orthogonal Latin squares (MOLSs) of order N. In particular, we…