Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

The entropy gain of quantum channels

Alexander Semenovich Holevo

Published Jul 1, 2011• 10 citations
Publisher

Abstract

In this paper we study the entropy gain H(Φ[ρ]) - H(ρ) for infinite-dimensional quantum channels Φ. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive, there are channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.

DOI
10.1109/isit.2011.6034107

Related papers

The entropy gain of infinite-dimensional quantum evolutions

A. S. Holevo

In the present paper we study the entropy gain $H(Φ[ρ])-H(ρ)$ for infinite-dimensional channels $Φ$. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty of channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.

arXiv:1003.5765•Doklady Mathematics•Oct 1, 2010•41 citations

Entropy Gain in ppp-Adic Quantum Channels

E. I. Zelenov

A configuration of a $$p$$ -adic quantum linear bosonic Gaussian channel is proposed. The entropy gain of such a channel is calculated. An adelic formula for the entropy gain is derived.

arXiv:2010.02750•Physics of Particles and Nuclei•Jul 1, 2020•8 citations

Superadditivity of the convex closure of the output entropy of a quantum channel

Максим Евгеньевич Широков

One of the main recent achievements of quantum information theory [1] is the proof of the equivalence of several (sub-, super-) additivity conjectures for finite-dimensional quantum channels and systems [2] (see the survey in [3]). The main purpose of this paper is to give a generalization of this result to the infinite-dimensional case. Let H and H ′ be separable Hilbert spaces. A quantum channel is a linear completely positive trace-preserving map Φ: T(H ) 7→ T(H ′), where T(H ) is the ideal of all trace class operators on H . In particular, Φ generates an affine map of the convex set S(H ) of states (that is, density operators) on the space H to the set S(H ′) of states on the space H ′ [1]. Important characteristics of a quantum channel are the output entropy HΦ(ρ) = H(Φ(ρ)), a lower-semicontinuous concave function on the input state space with values in [0,+∞], and its convex closure (see [4]), denoted by b HΦ(ρ) and called the b H-function of the channel Φ. It was shown in [5] that the convex closure of the output entropy of an arbitrary quantum channel Φ is given by the expression b HΦ(ρ) = inf μ Z

Russian Mathematical Surveys•Dec 31, 2006•2 citations

Gaussian classical-quantum channels: gain of entanglement-assistance

Alexander Semenovich Holevo

In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C

arXiv:1211.4774•Nov 20, 2012•2 citations

Gaussian classical-quantum channels: Gain from entanglement-assistance

Alexander Semenovich Holevo

In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; embedding of the classical input in quantum input is always possible, and therefore the classical entanglement-assisted capacity C ea under an appropriate input constraint is well defined. We prove the general property of entropy increase for a weak complementary channel, which implies the equality C = C ea (where C is the unassisted capacity) for a certain class of c-q Gaussian channels under an appropriate energy-type constraint. On the other hand, we show by an explicit example that the inequality C < C ea is not unusual for constrained c-q Gaussian channel.

Problems of Information Transmission•Jan 1, 2014•2 citations

Minimum output entropy of a non-Gaussian quantum channel

Laleh Memarzadeh, Stefano Mancini

We introduce a model of a non-Gaussian quantum channel that stems from the composition of two physically relevant processes occurring in open quantum systems, namely, amplitude damping and dephasing. For it we find input states approaching zero output entropy while respecting the input energy constraint. These states fully exploit the infinite dimensionality of the Hilbert space. Upon truncation of the latter, the minimum output entropy remains finite, and optimal input states for such a case are conjectured thanks to numerical evidence.

arXiv:1605.04525•Physical Review A•Aug 30, 2016•15 citations
In this paper we study the entropy gain H(Φ[ρ]) - H(ρ) for infinite-dimensional quantum channels Φ. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive, there are channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.
In the present paper we study the entropy gain H(Φ[ρ])−H(ρ)H(Φ[ρ])-H(ρ)H(Φ[ρ])−H(ρ) for infinite-dimensional channels ΦΦΦ. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty of channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.
A configuration of a ppp -adic quantum linear bosonic Gaussian channel is proposed. The entropy gain of such a channel is calculated. An adelic formula for the entropy gain is derived.
One of the main recent achievements of quantum information theory [1] is the proof of the equivalence of several (sub-, super-) additivity conjectures for finite-dimensional quantum channels and systems [2] (see the survey in [3]). The main purpose of this paper is to give a generalization of this result to the infinite-dimensional case. Let H and H ′ be separable Hilbert spaces. A quantum channel is a linear completely positive trace-preserving map Φ: T(H ) 7→ T(H ′), where T(H ) is the ideal of all trace class operators on H . In particular, Φ generates an affine map of the convex set S(H ) of states (that is, density operators) on the space H to the set S(H ′) of states on the space H ′ [1]. Important characteristics of a quantum channel are the output entropy HΦ(ρ) = H(Φ(ρ)), a lower-semicontinuous concave function on the input state space with values in [0,+∞], and its convex closure (see [4]), denoted by b HΦ(ρ) and called the b H-function of the channel Φ. It was shown in [5] that the convex closure of the output entropy of an arbitrary quantum channel Φ is given by the expression b HΦ(ρ) = inf μ Z
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; embedding of the classical input in quantum input is always possible, and therefore the classical entanglement-assisted capacity C ea under an appropriate input constraint is well defined. We prove the general property of entropy increase for a weak complementary channel, which implies the equality C = C ea (where C is the unassisted capacity) for a certain class of c-q Gaussian channels under an appropriate energy-type constraint. On the other hand, we show by an explicit example that the inequality C < C ea is not unusual for constrained c-q Gaussian channel.
We introduce a model of a non-Gaussian quantum channel that stems from the composition of two physically relevant processes occurring in open quantum systems, namely, amplitude damping and dephasing. For it we find input states approaching zero output entropy while respecting the input energy constraint. These states fully exploit the infinite dimensionality of the Hilbert space. Upon truncation of the latter, the minimum output entropy remains finite, and optimal input states for such a case are conjectured thanks to numerical evidence.