Related papers: Trace distance from the viewpoint of quantum opera…
We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be…
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…
Recently, trace distance measure of coherence has been proposed for characterizing the coherence of a given quantum state. However, it seems difficult to estimate the optimal incoherent state for high dimensional states. An explicit…
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…
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…
New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar…
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…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
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 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,…
Within the framework of quantum mechanics over a quadratic extension of the non-Archimedean field of p-adic numbers, we provide a definition of a quantum state relying on a general algebraic approach and on a p-adic model of probability…
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…
It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance. This is used to measure how far the state under investigation is from the closest "classical-quantum" one.…
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…
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…
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…
Distance to Uncontrollability is a crucial concept in classical control theory. Here, we introduce Quantum Distance to Uncontrollability as a measure how close a universal quantum system is to a non-universal one. This allows us to provide…
To implement quantum information technologies, carefully designed control for preparing a desired state plays a key role. However, in realistic situation, the actual performance of those methodologies is severely limited by decoherence.…
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…
In 2005, trace distance between an ideal quantum state to be distributed and an actual quantum state distributed was introduced as a valid security measure of Quantum Key Distribution (QKD) by R. Renner et al., then it has been perceived…