scholarly journals CALCULATING A MAXIMIZER FOR QUANTUM MUTUAL INFORMATION

2008 ◽  
Vol 06 (supp01) ◽  
pp. 745-750 ◽  
Author(s):  
T. C. DORLAS ◽  
C. MORGAN
Keyword(s):  
Mutual Information ◽  
State Capacity ◽  
Convex Combination ◽  
Product State ◽  
Not Given ◽  
Classical Information ◽  
Amplitude Damping Channel ◽  
Quantum Amplitude ◽  
Memoryless Channels ◽  
Quantum Mutual Information

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.

scholarly journals The locking-decoding frontier for generic dynamics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130289 ◽  
Author(s):  
Frédéric Dupuis ◽  
Jan Florjanczyk ◽  
Patrick Hayden ◽  
Debbie Leung
Keyword(s):  
Mutual Information ◽  
Quantum Key Distribution ◽  
Black Hole Physics ◽  
Quantum Systems ◽  
Classical Information ◽  
Accessible Information ◽  
Generic Dynamics ◽  
Quantum Mutual Information ◽  
Logarithmic Number ◽  
Quantum Key Distribution Protocol

It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. Finally, we exhibit a quantum key distribution protocol that is ‘secure’ in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others.

scholarly journals ENTANGLEMENT-ASSISTED CLASSICAL INFORMATION CAPACITY OF THE AMPLITUDE DAMPING CHANNEL

2003 ◽  
Vol 17 (29n30) ◽  
pp. 1547-1552
Author(s):  
XIAN-TING LIANG
Keyword(s):  
Mutual Information ◽  
Information Capacity ◽  
Dense Coding ◽  
Noisy Channels ◽  
Amplitude Damping ◽  
Covariant Quantum ◽  
Classical Information ◽  
Coding Scheme ◽  
Amplitude Damping Channel ◽  
The Difference

In this paper, we calculate the entanglement-assisted classical information capacity of the amplitude damping channel and compare it with the particular mutual information which is considered as the entanglement-assisted classical information capacity of this channel in Ref. 6. It is shown that the difference between them is very small. In addition, we point out that using partial symmetry and concavity of mutual information derived from the dense coding scheme, one can simplify the calculation of entanglement-assisted classical information capacities for non-unitary-covariant quantum noisy channels.

scholarly journals Rényi generalizations of the conditional quantum mutual information

2015 ◽  
Vol 56 (2) ◽  
pp. 022205 ◽  
Author(s):  
Mario Berta ◽  
Kaushik P. Seshadreesan ◽  
Mark M. Wilde
Keyword(s):  
Mutual Information ◽  
Quantum Mutual Information

Tensor Product State Capacity of Non-interacting Fermion Quantum Channel

2011 ◽  
Vol 40 (9) ◽  
pp. 1392-1396
Author(s):  
彭永刚 PENG Yong-gang ◽  
巩龙 GONG Long-yan
Keyword(s):  
Tensor Product ◽  
Quantum Channel ◽  
State Capacity ◽  
Product State

The classical capacity achievable by a quantum channel assisted by limited entanglement

2004 ◽  
Vol 4 (6&7) ◽  
pp. 537-545
Author(s):  
P.W. Shor
Keyword(s):  
Mutual Information ◽  
Quantum Channel ◽  
Density Matrices ◽  
Trade Off ◽  
Classical Capacity ◽  
Quantum Mutual Information

We give the trade-off curve showing the capacity of a quantum channel as a function of the amount of entanglement used by the sender and receiver for transmitting information. The endpoints of this curve are given by the Holevo-Schumacher-Westmoreland capacity formula and the entanglement-assisted capacity, which is the maximum over all input density matrices of the quantum mutual information. The proof we give is based on the Holevo-Schumacher-Westmoreland formula, and also gives a new and simpler proof for the entanglement-assisted capacity formula.

scholarly journals Correlations in Two-Qubit Systems under Non-Dissipative Decoherence

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 20
Author(s):  
Diego G. Bussandri ◽  
Tristán M. Osán ◽  
Pedro W. Lamberti ◽  
Ana P. Majtey
Keyword(s):  
Mutual Information ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Standard Quantum ◽  
Optimal Value ◽  
Quantum Mutual Information ◽  
Classical Correlations ◽  
Correlation Measures ◽  
Qubit States

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.

Sign in / Sign up

Export Citation Format

Share Document