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.

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.

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.

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.

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 Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel

2011 ◽  
Vol 57 (12) ◽  
pp. 8114-8126 ◽  
Author(s):  
Toby S. Cubitt ◽  
Jianxin Chen ◽  
Aram W. Harrow
Keyword(s):  
Quantum Channel ◽  
Classical Capacity

scholarly journals BB84 with Both Several Cloning and Intercept-resend Attacks

2018 ◽  
Vol 8 (5) ◽  
pp. 2988
Author(s):  
Mustapha Dehmani ◽  
El Mehdi Salmani ◽  
Hamid Ez-Zahraouy ◽  
Abdelilah Benyoussef
Keyword(s):  
Mutual Information ◽  
Quantum Channel ◽  
Quantum Error ◽  
Explicit Expressions

<p>The goal of the protocol QKD BB84 is to allow a transmitter and a receiver which uses a quantum channel to exchange their keys and to detect the presence of eavesdropping attacks. In the present research, we investigate the effect of several eavesdroppers with both intercept-resend and cloning attacks. We will propose the different possible cases of the positioning of the eavesdroppers and their strategies of attacks; also we will calculate the mutual information for each case. The explicit expressions of the mutual information and quantum error clearly show that the security of the exchanged information depends on the numbers of the eavesdroppers and their attacks parameters on the quantum channel.</p>

Upper bound on the classical capacity of a quantum channel assisted by classical feedback

2021 ◽  
Author(s):  
Dawei Ding ◽  
Sumeet Khatri ◽  
Yihui Quek ◽  
Peter W. Shor ◽  
Xin Wang ◽  
...  
Keyword(s):  
Upper Bound ◽  
Quantum Channel ◽  
Classical Capacity

QUANTUM KEY DISTRIBUTION WITH SEVERAL INTERCEPTS AND RESEND ATTACKS

2009 ◽  
Vol 23 (23) ◽  
pp. 4755-4765 ◽  
Author(s):  
HAMID EZ-ZAHRAOUY ◽  
ABDELILAH BENYOUSSEF
Keyword(s):  
Mutual Information ◽  
Quantum Channel ◽  
Quantum Key Distribution ◽  
Nonlinear Function ◽  
Upper Limit ◽  
Large N ◽  
Attack Phase ◽  
Error Behavior ◽  
Quantum Error ◽  
Good Agreement

The effect of several eavesdroppers intercept-resend attacks on the quantum error and mutual information between honest parties of a quantum channel chain is investigated within the BB84 (Bennett and Brassard, 1984). The quantum error and the mutual information are computed for arbitrary number of attacks. It is found that the quantum error and the secured–no secured transition depend strongly on the number N of eavesdroppers and their probabilities of intercepting attacks. For N = 3, numerical calculations show that the quantum error exhibits three kinds of different behaviors as a function of the probability of attack ω1of the first eavesdropper namely: (i) the quantum error remains constant for sufficiently small ω1, (ii) exhibits a plateau for intermediate values of ω1, (iii) increases, passes through a maximum and decreases when increasing ω1. However, depending on the probabilities of attack, phase diagrams present several kinds of topologies, in good agreement with the quantum error behavior. Moreover, in the particular case where all eavesdroppers intercept with identical probabilities ω, the quantum error increases as a nonlinear function with the number of eavesdroppers before reaching an upper limit of ≈ 0.475 for sufficiently large N. Besides, it is shown that the secured–no secured transition occurs under the effect of the number of eavesdroppers.

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