Classical capacity of a noiseless quantum channel assisted by noisy entanglement

2001 ◽  
Vol 1 (3) ◽  
pp. 70-78
Author(s):  
M Horodecki ◽  
P Horodecki ◽  
R l Horodecki ◽  
D Leung ◽  
B Terha
Keyword(s):  
Mutual Information ◽  
General Formula ◽  
Quantum Channel ◽  
Classical Case ◽  
Von Neumann Entropy ◽  
Entangled States ◽  
Von Neumann ◽  
Classical Capacity ◽  
Quantum Mutual Information

We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender's share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our results is that bound entangled states cannot increase the capacity of a noiseless quantum channel.

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 On Entangled Information and Quantum Capacity

2001 ◽  
Vol 08 (01) ◽  
pp. 1-18 ◽  
Author(s):  
Viacheslav P. Belavkin
Keyword(s):  
Quantum Channel ◽  
Simple Algebra ◽  
Von Neumann Entropy ◽  
Entangled States ◽  
Input State ◽  
Von Neumann ◽  
Quantum Capacity ◽  
Different Types ◽  
Mixed Compound ◽  
True Quantum

The pure quantum entanglement is generalized to the case of mixed compound states to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized as transpose-CP but not CP maps. The entangled information is introduced as the relative entropy of the mutual and the input state and total information of the entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the supremum of the information over all c-entanglements, and the true quantum entropy, which is achieved at the standard entanglement. The q-capacity, defined as the supremum over all entanglements, doubles the c-capacity in the case of the simple algebra. The conditional q-entropy is positive, and q-information of a quantum channel is additive.

Teleportation and dense coding via a multiparticle quantum channel of the GHZ-class

2002 ◽  
Vol 2 (5) ◽  
pp. 367-378
Author(s):  
V.N. Gorbachev ◽  
A.I. Zhiliba ◽  
A.I. Trubilko ◽  
A.A. Rodichkina
Keyword(s):  
Quantum Channel ◽  
Entangled States ◽  
Dense Coding ◽  
Ghz States ◽  
Classical Capacity ◽  
Coding Schemes ◽  
One To One

A set of protocols for teleportation and dense coding schemes based on a multiparticle quantum channel, represented by the $N$-particle entangled states of the GHZ class, is introduced. Using a found representation for the GHZ states, it was shown that for dense coding schemes enhancement of the classical capacity of the channel due from entanglement is $N/N-1$. Within the context of our schemes it becomes clear that there is no one-to one correspondence between teleportation and dense coding schemes in comparison when the EPR channel is exploited. A set of schemes, for which two additional operations as entanglement and disentanglement are permitted, is considered.

QUANTUM ENTROPY AND INFORMATION IN DISCRETE ENTANGLED STATES

2001 ◽  
Vol 04 (02) ◽  
pp. 137-160 ◽  
Author(s):  
VIACHESLAV P. BELAVKIN ◽  
MASANORI OHYA
Keyword(s):  
Conditional Entropy ◽  
Von Neumann Entropy ◽  
Entangled States ◽  
Commutative Case ◽  
Maximal Abelian Subalgebra ◽  
Von Neumann ◽  
Abelian Subalgebra ◽  
Different Types ◽  
Classical Quantum ◽  
Entropic Measure

Quantum entanglements, describing truly quantum couplings, are studied and classified for discrete compound states. We show that classical-quantum correspondences such as quantum encodings can be treated as d-entanglements leading to a special class of separable compound states. The mutual information for the d-compound and for q-compound (entangled) states leads to two different types of entropies for a given quantum state. The first one is the von Neumann entropy, which is achieved as the supremum of the information over all d-entanglements, and the second one is the dimensional entropy, which is achieved at the standard entanglement, the true quantum entanglement, coinciding with a d-entanglement only in the commutative case. The q-conditional entropy and q-capacity of a quantum noiseless channel, defined as the supremum over all entanglements, is given as the logarithm of the dimensionality of the input von Neumann algebra. It can double the classical capacity, achieved as the supremum over all semiquantum couplings (d-entanglements, or encodings), which is bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra. The entropic measure for essential entanglement is introduced.

scholarly journals Relating Entropies of Quantum Channels

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1028
Author(s):  
Dariusz Kurzyk ◽  
Łukasz Pawela ◽  
Zbigniew Puchała
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Quantum Channel ◽  
Von Neumann Entropy ◽  
Quantum Channels ◽  
Von Neumann ◽  
Channel One ◽  
Depolarizing Channel

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.

scholarly journals Hydrodynamics of quantum entropies in Ising chains with linear dissipation

2022 ◽  
Author(s):  
Vincenzo Alba ◽  
Federico Carollo
Keyword(s):  
Mutual Information ◽  
Hydrodynamic Limit ◽  
Transverse Field ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Simple Description ◽  
Von Neumann ◽  
Long Time ◽  
Dynamics Of Correlations ◽  
Quasiparticle Picture

Abstract We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities —such as the von Neumann entropy, the Rényi entropies, and the associated mutual information— admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.

Quantum state sharing with mixing state from six-qubit entangled pure one

2020 ◽  
Vol 35 (32) ◽  
pp. 2050264
Author(s):  
Zhanjun Zhang ◽  
Hao Yuan ◽  
Chuanmei Xie ◽  
Biaoliang Ye
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Pure State ◽  
Essential Role ◽  
Entangled States ◽  
Entangled State ◽  
Quantum State Sharing ◽  
Mixing State ◽  
Preliminary Study

In this paper the possibility of using mixing entangled states as quantum channel to accomplish quantum state sharing (QSTS) is considered. As a preliminary study, an efficient tripartite QSTS scheme is put forward by utilizing a mixing entangled state, which is a derivative of a six-qubit entangled pure state under a two-qubit confusion. Some specific discussions about the QSTS scheme are made, including the issues of the scheme determinacy, the sharer symmetry, the scheme security and the essential role of quantum channel as well as the current experimental feasibility.

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 Local extrema of entropy functions under tensor products

2011 ◽  
Vol 11 (11&12) ◽  
pp. 1028-1044
Author(s):  
Shmuel Friedland ◽  
Gilad Gour ◽  
Aidan Roy
Keyword(s):  
Quantum Channel ◽  
Tensor Products ◽  
Von Neumann Entropy ◽  
Local Minima ◽  
Von Neumann ◽  
Local Commutativity ◽  
Local Extrema ◽  
Dimension 2 ◽  
Entropy Functions

We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products if one of the subspaces has dimension 2.

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