Related papers: Partitioned trace distances
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport…
The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
Introducing contravariant trace-densities for quantum states, we restore one to one correspondence between quantum operations described by normal CP maps and their trace densities as Hermitian positive operator-valued contravariant kernels.…
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…
Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual…
In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in…
Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states…
Based upon the newly proposed partial quantum statistics [T. Zhou, Solid State Commun. 115, 185 (2000)], some canonical physical properties of partially localized electron systems have been calculated. The calculated transport and…
We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an ad…
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…
In this work we examine recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We further study possibilities to reduce the quantum resources without any efficiency…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in…
A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…