Almost all quantum channels are equidistant

Nechita, Ion; Puchała, Zbigniew; Pawela, Łukasz; Życzkowski, Karol

doi:10.1063/1.5019322

Cited by 33 publications

(43 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a large N a typical channel becomes close to a one-step contraction, which sends any state into the single invariant state, Φ(ρ) = ρ inv = Φ(ρ inv ). It is known [41] that a generic channel is close to be unital and the correction term, Φ(1l) − 1l, behaves like a random hermitian matrix of the Gaussian unitary ensemble with asymptotically vanishing norm.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Universal Spectra of Random Lindblad Operators

et al. 2019

Self Cite

View full text Add to dashboard Cite

To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties of these operators, including the shape of the spectrum in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate universality of the spectral features. The notion of ensemble of random generators of Markovian qauntum evolution constitutes a step towards categorization of dissipative quantum chaos.

show abstract

mentioning

confidence: 99%

“…The matrix G R of size N 2 is taken from the real Ginibre ensemble. The correction term C approximates X by a symmetric GOE matrix [41] of size N . Matrices are normalized as TrG R G † R = N 2 , so that its spectrum covers uniformly a disk of radius 1, while TrC 2 = N/4 assures that its density forms the Wigner semicircle of radius 1.…”

mentioning

confidence: 99%

Universal Spectra of Random Lindblad Operators

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…For Hermiticity preserving Φ, we have the following well-known bounds for the diamond norm [9,17,19] 1…”

Section: φ Is Trace-preserving If and Only If Trmentioning

confidence: 99%

“…This input state is what we call "the strategy" for discriminating quantum channels. Due to the complicated structure of the set of quantum channels, the problem has been studied in the limit of large input and output dimensions [9]. In this paper we focus on the problem of discriminating quantum measurements which are viewed as a subclass of quantum channels.…”

Section: Introductionmentioning

confidence: 99%

Strategies for optimal single-shot discrimination of quantum measurements

et al. 2018

Self Cite

View full text Add to dashboard Cite

In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance between the measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product, the program finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.

show abstract

“…When dim(Z) = dim(X ) dim(Y) this is known to generate a uniform distribution over the set of quantum channels [37,38]. The implementation uses the type ChoiJamiolkowskiMatrices{β,K}.…”

Section: Random Quantum Channelsmentioning

confidence: 99%

QuantumInformation.jl—A Julia package for numerical computation in quantum information theory

2018

Self Cite

View full text Add to dashboard Cite

Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is little effort in implementing this kind of tools in the language. is a modern programming language designed for numerical computation with excellent support for vector and matrix algebra, extended type system that allows for implementation of elegant application interfaces and support for parallel and distributed computing. is a new quantum information theory library implemented in that provides functions for creating and analyzing quantum states, and for creating quantum operations in various representations. An additional feature of the library is a collection of functions for sampling random quantum states and operations such as unitary operations and generic quantum channels.

show abstract

Almost all quantum channels are equidistant

Cited by 33 publications

References 46 publications

Universal Spectra of Random Lindblad Operators

Universal Spectra of Random Lindblad Operators

Strategies for optimal single-shot discrimination of quantum measurements

QuantumInformation.jl—A Julia package for numerical computation in quantum information theory

Contact Info

Product

Resources

About