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

arXiv:0904.3794

Quantum Tsallis entropy and projective measurement

Marko V. Jankovic

Published Apr 24, 2009• 0 citations
arXivHTMLPDF

Abstract

It is well known that projective measurement will not decrease the von Neumann entropy of a quantum state. In this paper, it is shown that projective measurement will not decrease the quantum Tsallis entropy of a quantum state, either. Using a similar analysis, it can be shown that projective measurement will not decrease the quantum unified (r, s)-entropy in general.

DOI
10.48550/arxiv.0904.3794

Related papers

Quantum Kaniadakis entropy under projective measurement

Kamel Ourabah, Amel Hiba Hamici-Bendimerad, Mouloud Tribeche

It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property.

Physical Review E•Sep 10, 2015•17 citations

Generalized ‘Useful’ Relative Information Measures of Type (α, β)

Satish Kumar, Arun Choudhary

In this paper we define some new generalized measures of ‘useful’ relative information and study their particular cases. We also obtain their relations with common entropy measures. Moreover, we define the quantum generalized Tsallis entropy and show that projective measurement does not decrease the quantum generalized Tsallis entropy of a quantum state. Finally, we define generalized quantum Tsallis and Renyi relative entropies and discuss their particular cases.

Open Systems & Information Dynamics•Mar 1, 2015•0 citations

Exponential Quantum Tsallis Havrda Charvat Entropy of Type Alpha

Dhanesh Garg, Staish Kumar

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannons entropy is just the size of the sample space when the distribution is uniform. In this paper, we introduce a quantity which is called exponential Tsallis Havrda Charvat entropy and discuss its some properties. Further, we gave the application of exponential Tsallis Havrda Charvat entropy in quantum information theory which is called exponential quantum Tsallis Havrda Charvat entropy with its some major properties such as non-negative, concavity and continuity. It is found that projective measurement will not decrease the quantum entropy of a quantum state and at the end of the paper gave an upper bound on the quantum exponential entropy in terms of ensembles of pure state.

arXiv:1506.05557•Jun 18, 2015•0 citations

State reduction, information and entropy in quantum measurement processes

Masashi Ban

Information obtained by a quantum measurement process performed on a physical system and the entropy change of the measured physical system are considered in detail. It is shown that the condition for the amount of information obtained by the quantum measurement process to be represented by the Shannon mutual entropy is that the intrinsic observable of the measured physical system commutes with the operational observable defined by the quantum measurement process. When some measurement outcome is obtained, the decrease of the Shannon entropy of the measured system is compared with that of the von Neumann entropy. Furthermore, a condition is established under which the amount of information that can be established by the quantum measurement process becomes equal to the decrease of the Shannon entropy of the measured physical system.

Journal of Physics A Mathematical and General•Jan 1, 1999•10 citations

Quantum entropies, Schur concavity and dynamical semigroups

Paolo Aniello

Entropy plays a fundamental role in several branches of physics. In the quantum setting, one usually considers the von Neumann entropy, but other useful quantities have been proposed in the literature; e.g., the Rényi and the Tsallis entropies. The evolution of an open quantum system, described by a semigroup of dynamical maps (in short, a dynamical semigroup), may decrease a quantum entropy, for some initial condition. We will discuss various characterizations of those dynamical semigroups that, for every initial condition, do not decrease a general class of quantum entropies, which is defined using the notion of Schur concavity of a function. We will not assume that such a dynamical semigroup be completely positive, the physical justification of this condition being controversial. Therefore, we will consider semigroups of trace-preserving, positive — but not necessarily completely positive — linear maps. We will next focus on a special class of (completely positive) dynamical semigroups, the twirling semigroups , having applications in quantum information science. We will argue that the whole class of dynamical semigroups that do not decrease a quantum entropy can be obtained as a suitable generalization of the twirling semigroups.

Journal of Physics Conference Series•Jan 1, 2017•5 citations

Characterizing the dynamical semigroups that do not decrease a quantum entropy

Paolo Aniello, Dariusz Chruściński

Abstract In finite dimensions, we provide characterizations of the quantum dynamical semigroups that do not decrease the von Neumann, the Tsallis and the Rényi entropies, as well as a family of functions of density operators strictly related to the Schatten norms. A few remarkable consequences—in particular, a description of the associated infinitesimal generators—are derived, and some significant examples are discussed. Extensions of these results to semigroups of trace-preserving positive (i.e., not necessarily completely positive) maps and to a more general class of quantum entropies are also considered.

arXiv:1601.07808•Journal of Physics A Mathematical and Theoretical•Jul 14, 2016•14 citations
It is well known that projective measurement will not decrease the von Neumann entropy of a quantum state. In this paper, it is shown that projective measurement will not decrease the quantum Tsallis entropy of a quantum state, either. Using a similar analysis, it can be shown that projective measurement will not decrease the quantum unified (r, s)-entropy in general.
Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannons entropy is just the size of the sample space when the distribution is uniform. In this paper, we introduce a quantity which is called exponential Tsallis Havrda Charvat entropy and discuss its some properties. Further, we gave the application of exponential Tsallis Havrda Charvat entropy in quantum information theory which is called exponential quantum Tsallis Havrda Charvat entropy with its some major properties such as non-negative, concavity and continuity. It is found that projective measurement will not decrease the quantum entropy of a quantum state and at the end of the paper gave an upper bound on the quantum exponential entropy in terms of ensembles of pure state.
Information obtained by a quantum measurement process performed on a physical system and the entropy change of the measured physical system are considered in detail. It is shown that the condition for the amount of information obtained by the quantum measurement process to be represented by the Shannon mutual entropy is that the intrinsic observable of the measured physical system commutes with the operational observable defined by the quantum measurement process. When some measurement outcome is obtained, the decrease of the Shannon entropy of the measured system is compared with that of the von Neumann entropy. Furthermore, a condition is established under which the amount of information that can be established by the quantum measurement process becomes equal to the decrease of the Shannon entropy of the measured physical system.
Entropy plays a fundamental role in several branches of physics. In the quantum setting, one usually considers the von Neumann entropy, but other useful quantities have been proposed in the literature; e.g., the Rényi and the Tsallis entropies. The evolution of an open quantum system, described by a semigroup of dynamical maps (in short, a dynamical semigroup), may decrease a quantum entropy, for some initial condition. We will discuss various characterizations of those dynamical semigroups that, for every initial condition, do not decrease a general class of quantum entropies, which is defined using the notion of Schur concavity of a function. We will not assume that such a dynamical semigroup be completely positive, the physical justification of this condition being controversial. Therefore, we will consider semigroups of trace-preserving, positive — but not necessarily completely positive — linear maps. We will next focus on a special class of (completely positive) dynamical semigroups, the twirling semigroups , having applications in quantum information science. We will argue that the whole class of dynamical semigroups that do not decrease a quantum entropy can be obtained as a suitable generalization of the twirling semigroups.
Abstract In finite dimensions, we provide characterizations of the quantum dynamical semigroups that do not decrease the von Neumann, the Tsallis and the Rényi entropies, as well as a family of functions of density operators strictly related to the Schatten norms. A few remarkable consequences—in particular, a description of the associated infinitesimal generators—are derived, and some significant examples are discussed. Extensions of these results to semigroups of trace-preserving positive (i.e., not necessarily completely positive) maps and to a more general class of quantum entropies are also considered.