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The Capacity of Quantum Channel with General Signal States
Quantum Physics · Submitted 14 Nov 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions.
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The abstract, sentence by sentence
It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the pure state channel.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. | result 0.99 | 0.87 | 0.94 | asserted 1.00 |
| s1 | This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the pure state channel. | background 0.62 | 0.19 | 0.07 | asserted 1.00 |
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The paper
Original abstract
It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals to the maximum of the entropy bound with respect to all apriori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the pure state channel.
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References
How the literature uses it
36 arXiv papers cite this in 56 sentences
Papers citing it · 29 sentences without a confident label
Uses its method or tool 2 papers
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Now, this is also an achievable rate per unit cost since for any ${ p_X, ρ_A(x) }$, we can achieve a rate per channel use $I(X;B)_ρ$ using cost-constrained Holevo-Schumacher-Westmoreland (HSW) coding [ref] .
Quantum Channel Capacities Per Unit Cost · Classical Communication · 0.87
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The approach given by [ref] is to multiplex the channel such that one use of this multiplexed channel corresponds to multiple uses of the original channel.
Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels · Introduction · 0.88
Compares with it 2 papers
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The error analysis at the relay is similar to that of the Holevo-Schumacher-Westmoreland theorem [ref] .
Network information theory for classical-quantum channels · Achievability proof · 0.89
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For now, we should regard our contribution in this paper as a more explicit method for achieving the Holevo information rate (as compared to those from prior work [ref] ).
Polar codes for classical-quantum channels · Introduction · 0.91
Cites it as background 19 papers
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The classical capacity $C()$ of $$ is given by the regularized Holevo information [ref] : [equation] We say that a quantum channel $$ has weakly additive Holevo information if [equation] holds for all $n∈ℕ$.
Approaches for approximate additivity of the Holevo information of quantum channels · Holevo information and classical capacity of quantum channels · 0.96
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The classical capacity is defined as the maximum rate at which it is possible to send classical data over a quantum channel such that the error probability decreases to zero in the limit of many independent uses of the channel [ref] .
Strong converse for the classical capacity of optical quantum communication channels · Introduction · 0.98
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Holevo, Schumacher, and Westmoreland (HSW) [ref] characterized the classical capacity of a quantum channel $𝒩$ in terms of the following formula: [equation] where ${ p_X( x) ,ρ_x}$ is an ensemble of quantum states, $I( X;B) _ρ≡H( X) _ρ+H( B) _ρ-H( XB) _ρ$ is the quantum mutual information, and $H( A) _σ≡-$Tr${ σlogσ}$ is the von Neumann entropy of a state $σ$ defined on system $A$.[Unless stated otherwise, $log$ always denotes the base two logarithm.] In the above formula, the quantum mutual information $I( X;B)$ is computed with respect to the following classical-quantum state: [equation] for some orthonormal basis ${ |x⟩}$, and the notation $𝒩_A→B$ indicates that the channel accepts an input on the system $A$ and outputs to the system $B$.
Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy · Introduction · 0.97
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