Related papers: Estimation of trace distance between two arbitrary…
In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an…
The trace distance between two quantum states, $\rho$ and $\sigma$, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of $\rho - \sigma$. In…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modified measure and the extended measure for bipartite states. We…
We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…
The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…
A measure of quantum non-Markovianity for an open system dynamics, based on revivals of the distinguishability between system states, has been introduced in the literature using the trace distance as quantifier for distinguishability.…
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error $\epsilon$ in trace distance required…
In machine learning and particularly in topological data analysis, $\epsilon$-graphs are important tools but are generally hard to compute as the distance calculation between n points takes time O(n^2) classically. Recently, quantum…
The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable…
Quantum state comparison, utilizing metrics like fidelity and trace distance, underpins the assessment of quantum networks within quantum information theory. While recent research has expanded theoretical understanding, incorporating error…
Gaussian states of bosonic quantum systems enjoy numerous technological applications and are ubiquitous in nature. Their significance lies in their simplicity, which in turn rests on the fact that they are uniquely determined by two…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…
We show that the quantum measurement known as the pretty good measurement can be used to identify an unknown quantum state picked from any set of $n$ mixed states that have pairwise fidelities upper-bounded by a constant below 1, given…
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact…
Properties of random mixed states of order $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states…
We study the computational complexity of estimating the quantum $\ell_{\alpha}$ distance ${\mathrm{T}_\alpha}(\rho_0,\rho_1)$, defined via the Schatten $\alpha$-norm $\|A\|_{\alpha} = \mathrm{tr}(|A|^{\alpha})^{1/\alpha}$, given…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…