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

TRANSFORMATIONS ON DENSITY OPERATORS THAT LEAVE THE HOLEVO BOUND INVARIANT

Oliver Nagy

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

For a given probability distribution 1;:::; m we deter- mine the structure of all such maps dened on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy S( m X k=1 k ( k)) m X k=1 kS( ( k)) = S( m X k=1 k k) m X k=1 kS( k) for all possible collections 1;:::; m of density operators. The Holevo bound (or Holevo information) plays a distinguished role in quantum information theory. It provides an upper limit (which can be achieved in certain cases) of the accessible information in a quantum mea- surement, it gives an upper bound on how well we can infer the value of an unknown random variable based on the knowledge of another one. The denition

Related papers

Transformations on Density Operators That Leave the Holevo Bound Invariant

Lajos Molnár, Gergő Nagy

International Journal of Theoretical Physics•May 18, 2013•5 citations

TRANSFORMATIONS ON DENSITY OPERATORS PRESERVING GENERALISED ENTROPY OF A CONVEX COMBINATION

Marcell Gaál, Gergő Nagy

We aim to characterise those transformations on the set of density operators (which are the mathematical representatives of the states in quantum information theory) that preserve a so-called generalised entropy ofonefixed convex combination of operators. The characterisation strengthens a recent result of Karder and Petek where the preservation of the same quantity was assumed forallconvex combinations.

Bulletin of the Australian Mathematical Society•May 3, 2018•1 citation

Universal upper bound for the Holevo information induced by a quantum operation

Lin Zhang, Junde Wu, Shao-Ming Fei

arXiv:1110.5979•Physics Letters A•Oct 11, 2012•4 citations

Hierarchy of bounds on accessible information and informational power

Michele Dall’Arno

Quantum theory imposes fundamental limitations on the amount of information that can be carried by any quantum system. On the one hand, the Holevo bound rules out the possibility of encoding more information in a quantum system than in its classical counterpart, comprised of perfectly distinguishable states. On the other hand, when states are uniformly distributed in the state space, the so-called subentropy lower bound is saturated. How uniform quantum systems are can be naturally quantified by characterizing them as $t$-designs, with $t=\ensuremath{\infty}$ corresponding to the uniform distribution. Here we show the existence of a trade-off between the uniformity of a quantum system and the amount of information it can carry. To this aim, we derive a hierarchy of informational bounds as a function of $t$ and prove their tightness for qubits and qutrits. By deriving asymptotic formulas for large dimensions, we also show that the statistics generated by any $t$-design with $t>1$ contains no more than a single bit of information, and this amount decreases with $t$. Holevo and subentropy bounds are recovered as particular cases for $t=1$ and $t=\ensuremath{\infty}$, respectively.

arXiv:1504.04429•Physical Review A•Jul 27, 2015•12 citations

Upper Bounds for the Holevo Information Quantity and Their Use

Максим Евгеньевич Широков

We present a family of easily computable upper bounds for the Holevo (information) quantity of an ensemble of quantum states depending on a reference state (as a free parameter). These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve the estimates existing in the literature. We also present an upper bound for the Holevo quantity of a generalized ensemble of quantum states with finite average energy depending on the metric divergence of an ensemble. In the case of a multi-mode quantum oscillator, this upper bound is tight for large energy. Upper bounds for the Holevo capacity of finite-dimensional quantum channels depending on metric characteristics of the channel output are obtained.

Problems of Information Transmission•Jul 1, 2019•3 citations

The optimal positive operator-valued measure for state discrimination

Wei Li, Shengmei Zhao

Evaluating the amount of information obtained from non-orthogonal quantum states is an important topic in the field of quantum information. The commonly used evaluation method is Holevo bound, which only provides a loose upper bound for quantum measurement. In this paper, we provide a theoretical study of the positive operator-valued measure (POVM) for discriminating nonorthogonal states. We construct a generalized POVM measurement operation, and derive the optimal one for state discrimination by Lagrange multiplier method. With simulation, we find that the optimal POVM measurement provides a tight upper bound for state discrimination, which is significantly lower than that predicted by Holevo bound. The derivation of optimal POVM measurement will play an important role in the security research of quantum key distribution.

arXiv:2108.10474•Aug 24, 2021•0 citations
For a given probability distribution 1;:::; m we deter- mine the structure of all such maps dened on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy S( m X k=1 k ( k)) m X k=1 kS( ( k)) = S( m X k=1 k k) m X k=1 kS( k) for all possible collections 1;:::; m of density operators. The Holevo bound (or Holevo information) plays a distinguished role in quantum information theory. It provides an upper limit (which can be achieved in certain cases) of the accessible information in a quantum mea- surement, it gives an upper bound on how well we can infer the value of an unknown random variable based on the knowledge of another one. The denition
Quantum theory imposes fundamental limitations on the amount of information that can be carried by any quantum system. On the one hand, the Holevo bound rules out the possibility of encoding more information in a quantum system than in its classical counterpart, comprised of perfectly distinguishable states. On the other hand, when states are uniformly distributed in the state space, the so-called subentropy lower bound is saturated. How uniform quantum systems are can be naturally quantified by characterizing them as ttt-designs, with $t=\ensuremath{\infty}$ corresponding to the uniform distribution. Here we show the existence of a trade-off between the uniformity of a quantum system and the amount of information it can carry. To this aim, we derive a hierarchy of informational bounds as a function of ttt and prove their tightness for qubits and qutrits. By deriving asymptotic formulas for large dimensions, we also show that the statistics generated by any ttt-design with t>1t>1t>1 contains no more than a single bit of information, and this amount decreases with ttt. Holevo and subentropy bounds are recovered as particular cases for t=1t=1t=1 and $t=\ensuremath{\infty}$, respectively.
We present a family of easily computable upper bounds for the Holevo (information) quantity of an ensemble of quantum states depending on a reference state (as a free parameter). These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve the estimates existing in the literature. We also present an upper bound for the Holevo quantity of a generalized ensemble of quantum states with finite average energy depending on the metric divergence of an ensemble. In the case of a multi-mode quantum oscillator, this upper bound is tight for large energy. Upper bounds for the Holevo capacity of finite-dimensional quantum channels depending on metric characteristics of the channel output are obtained.
Evaluating the amount of information obtained from non-orthogonal quantum states is an important topic in the field of quantum information. The commonly used evaluation method is Holevo bound, which only provides a loose upper bound for quantum measurement. In this paper, we provide a theoretical study of the positive operator-valued measure (POVM) for discriminating nonorthogonal states. We construct a generalized POVM measurement operation, and derive the optimal one for state discrimination by Lagrange multiplier method. With simulation, we find that the optimal POVM measurement provides a tight upper bound for state discrimination, which is significantly lower than that predicted by Holevo bound. The derivation of optimal POVM measurement will play an important role in the security research of quantum key distribution.