Related papers: Partitioned trace distances
A family of quantum measures like the Shannon distinguishability is presented. These measures are defined over the two classes of POVM measurements and related to separate parts in the expression for mutual information. Changes of Ky Fan's…
Basic properties of Uhlmann's partial fidelities are discussed. Statistical interpretation in terms of POVM measurements is established. Multiplicativity properties are considered. The relationship between partial fidelities and partitioned…
In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states,…
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…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
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.…
Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations between the notions of unitarity, complete positivity,…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature.…
Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined. The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases. The obtained…
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…
When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace…
The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical…
Information is an inherent component of stochastic processes and to measure the distance between different stochastic processes it is not sufficient to consider the distance between their laws. Instead, the information which accumulates…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the…
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
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…
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…