Related papers: Monge Distance between Quantum States

Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…

Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…

This paper treats the isometries of metric spaces of quantum states. We consider two metrics on the set all quantum states, namely the Bures metric and the one which comes from the trace-norm. We describe all the corresponding (nonlinear)…

We develop a comprehensive axiomatic framework for quantum-inspired distance metrics on projective Hilbert spaces, providing a unified foundation that organizes and generalizes existing measures in quantum information theory. Starting from…

The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…

Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to…

Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…

The aim of the present note is to show that the method of our paper ArXiv:2408.11400 with minor extra efforts can be extended to obtain upper bounds for the Bures distance between quantum Gaussian states. We argue that these bounds are…

In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…

The optimal discrimination of non-orthogonal quantum states with minimum error probability is a fundamental task in quantum measurement theory as well as an important primitive in optical communication. In this work, we propose and…

We demonstrate the simple and deep equivalence between quantum coherence and nonclassicality and the definite way in which they determine metrological resolution. Moreover, we define a coherence observable consistent with a classical…

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated…

Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this article, we propose a fidelity based valid measure of purity and coherence monotone and establish a relationship…

In the literature, there have been several methods and definitions for working out if two theories are "equivalent" (essentially the same) or not. In this article, we do something subtler. We provide means to measure distances (and explore…

With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the complex projective space $\mathbb{P}(\mathbb{C}^n)$ modelling the space of pure states of an $n$-level…

Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…

In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find…

We set up a general theory for a quantum Wasserstein distance of order 1 in an operator algebraic framework, extending recent work in finite dimensions. In addition, this theory applies not only to states, but also to channels, giving a…

We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the…

This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard…