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

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.

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.

Quantum mutual information matrices

2017 ◽  
Vol 15 (01) ◽  
pp. 1750005
Author(s):  
Feng Liu
Keyword(s):  
Mutual Information ◽  
Information Matrix ◽  
Positive Semidefinite ◽  
Text Entry ◽  
Classical Counterpart ◽  
State Formula ◽  
Quantum Mutual Information ◽  
Multipartite States ◽  
Information Matrices

For any [Formula: see text]-partite state [Formula: see text], we define its quantum mutual information matrix as an [Formula: see text][Formula: see text][Formula: see text][Formula: see text][Formula: see text] matrix whose [Formula: see text]-entry is given by quantum mutual information [Formula: see text]. Although each entry of quantum mutual information matrix, like its classical counterpart, is also used to measure bipartite correlations, the similarity ends here: quantum mutual information matrices are not always positive semidefinite even for collections of up to 3-partite states. In this work, we define the genuine n-partite mutual information which can be easily calculated. This definition is symmetric, nonnegative, bounded and more accurate for measuring multipartite states.

scholarly journals Quantum Mutual Information Capacity for High-Dimensional Entangled States

2012 ◽  
Vol 108 (14) ◽  
Author(s):  
P. Ben Dixon ◽  
Gregory A. Howland ◽  
James Schneeloch ◽  
John C. Howell
Keyword(s):  
Mutual Information ◽  
Information Capacity ◽  
High Dimensional ◽  
Entangled States ◽  
Quantum Mutual Information

scholarly journals Non-monogamy of quantum discord and upper bounds for quantum correlation

2013 ◽  
Vol 13 (5&6) ◽  
pp. 469-478
Author(s):  
Xi-Jun Ren ◽  
Heng Fan
Keyword(s):  
Mutual Information ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Upper Bounds ◽  
Physical Analysis ◽  
Classical Correlation ◽  
Entanglement Of Formation ◽  
Quantum Mutual Information ◽  
Bipartite States

We consider a monogamy inequality of quantum discord in a pure tripartite state and show that it is equivalent to an inequality between quantum mutual information and entanglement of formation of two parties. Since this inequality does not hold for arbitrary bipartite states, quantum discord can generally be both monogamous and polygamous. We also carry out numerical calculations for some special states. The upper bounds of quantum discord and classical correlation are also discussed and we give physical analysis on the invalidness of a previous conjectured upper bound of quantum correlation. Our results provide new insights for further understanding of distributions of quantum correlations.

scholarly journals Long-distance entanglement in Motzkin and Fredkin spin chains

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Luca Dell'Anna
Keyword(s):  
Mutual Information ◽  
Entanglement Entropy ◽  
Ground States ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Long Distance ◽  
Half Integer ◽  
Quantum Mutual Information

We derive some entanglement properties of the ground states for two classes of quantum spin chains described by the Fredkin model, for half-integer spins, and the Motzkin model, for integer ones. Since the ground states of the two models are known analytically, we can calculate exactly the entanglement entropy, the negativity and the quantum mutual information. We show, in particular, that these systems exhibit long-distance entanglement, namely two disjoint regions of the chains remain entangled even when their separation is sent to infinity, i.e. these systems are not affected by decoherence. This strongly entangled behavior, Finally, we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains.

Sign in / Sign up

Export Citation Format

Share Document