相关论文: Trace distance from the viewpoint of quantum opera…

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretely selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and…

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for…

It is shown that the observability of a large class of operations on mixed states is fundamentally limited. We consider trace preserving, unital operations. This class includes unitary and perfect premeasurement operations. An upper bound…

In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient…

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.…

Cryptographic security of quantum key distribution is currently based on a trace distance criterion. The widespread misinterpretation of the criterion as failure probability and also its actual scope have been discussed previously. Recently…

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…

Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is…

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent…

A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…

This article studies quantum mechanical entanglement. We begin by illustrating why entanglement implies action at a distance. We then introduce a simple criterion for determining when a pure quantum state is entangled. Finally, we present a…

We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from…

With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate…

We thoroughly analyse the distance between quantum states that has been applied to state-dependent cloning and partly studied in the previous work of the author [Phys. Rev. A 66, 042304 (2002)]. Elementary proofs of its significant…

We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the…

Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…

We use an alternative approach to study the quantum phase transition in a coupled cavity lattice at finite temperature. As an illustrative example, we investigate the behaviors of the trace distance and quantum phase transition in a…

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.…

Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.