English
Related papers

Related papers: A de Finetti representation theorem for infinite d…

200 papers

Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements one can get a…

Quantum Physics · Physics 2017-05-16 Fernando G. S. L. Brandao , Aram W. Harrow

De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and…

Quantum Physics · Physics 2023-11-16 Sam Staton , Ned Summers

We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the…

Quantum Physics · Physics 2013-07-08 V. S. Shchesnovich , D. S. Mogilevtsev

Proving the unconditional security of a quantum key distribution (QKD) scheme is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for…

Quantum Physics · Physics 2010-03-15 Anthony Leverrier , Evgueni Karpov , Philippe Grangier , Nicolas J. Cerf

A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…

Information Theory · Computer Science 2021-06-28 Lampros Gavalakis , Ioannis Kontoyiannis

The aim of device-independent quantum key distribution (DIQKD) is to study protocols that allow the generation of a secret shared key between two parties under minimal assumptions on the devices that produce the key. These devices are…

Quantum Physics · Physics 2023-09-01 Sven Jandura , Ernest Y. -Z. Tan

In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…

Quantum Physics · Physics 2009-11-10 Christopher A. Fuchs , Ruediger Schack , Petra F. Scudo

Establishing the security of continuous-variable quantum key distribution against general attacks in a realistic finite-size regime is an outstanding open problem in the field of theoretical quantum cryptography if we restrict our attention…

Quantum Physics · Physics 2017-05-17 Anthony Leverrier

We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to…

Operator Algebras · Mathematics 2009-11-13 Claus Köstler , Roland Speicher

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…

Quantum Physics · Physics 2011-03-16 Giulio Chiribella

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective…

Quantum Physics · Physics 2009-11-13 Valerio Scarani , Renato Renner

A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…

Information Theory · Computer Science 2024-04-29 Mario Berta , Lampros Gavalakis , Ioannis Kontoyiannis

Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for…

Quantum Physics · Physics 2016-08-17 Frédéric Bouchard , Robert Fickler , Robert W Boyd , Ebrahim Karimi

We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…

Quantum Physics · Physics 2019-03-06 T. Hashimoto , A. Hayashi , M. Horibe

We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor…

Quantum Physics · Physics 2009-11-13 Matthias Christandl , Robert Koenig , Graeme Mitchison , Renato Renner

The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there…

Quantum Physics · Physics 2009-11-11 Mark S. Byrd

We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to…

Quantum Physics · Physics 2013-01-29 Anthony Leverrier , Raúl García-Patrón , Renato Renner , Nicolas J. Cerf

The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…

Quantum Physics · Physics 2017-08-23 Christopher A. Fuchs , Ruediger Schack

We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…

Quantum Physics · Physics 2024-11-15 Omar Fawzi , Richard Kueng , Damian Markham , Aadil Oufkir

An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…

Quantum Physics · Physics 2024-11-01 M. E. Shirokov