Related papers: Randomization theorems for quantum channels

The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in…

A parametrized family of normal states on a von Neumann algebra is called a statistical experiment, which generalizes the corresponding concepts in classical statistics and finite-dimensional quantum systems. We introduce randomization…

Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…

This paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k…

The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…

The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…

We study the problem of binary composite channel discrimination in the asymmetric setting, where the hypotheses are given by fairly arbitrary sets of channels, and samples do not have to be identically distributed. In the case of quantum…

We consider the family of energy-constrained diamond norms on the set of Hermitian-preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from this family generates the strong…

It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…

The capability of a given channel to communicate information is, a priori, distinct from its capability to distribute shared randomness. In this article we define randomness distribution capacities of quantum channels assisted by forward,…

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete…

Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

In this paper we introduce a new partial order on quantum states that considers which states can be achieved from others by updating on `agreeing' Bayesian evidence. We prove that this order can also be interpreted in terms of minimising…

The concept of $\e$-randomizing quantum channels has been introduced by Hayden, Leung, Shor and Winter in connection with approximately encrypting quantum states. They proved using a discretization argument that sets of roughly $d \log d$…

We extend the recent proof of the Generalized Quantum Stein's Lemma by Hayashi and Yamasaki [arXiv:2408.02722] to classical-quantum (c-q) channels. We analyze the composite hypothesis testing problem of testing a c-q channel…

In the developing theory of infinite-dimensional quantum channels the relevance of the energy-constrained diamond norms was recently corroborated both from physical and information-theoretic points of view. In this paper we study necessary…

Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for…

A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the…

A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…