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43
The capacity of a quantum channel for simultaneous transmission of classical and quantum information
, 2008
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Black holes as mirrors: quantum information in random subsystems
 Journal of High Energy Physics
"... We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past th ..."
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Cited by 50 (3 self)
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We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the “halfway ” point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the halfway point remains concealed until the halfway point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum errorcorrecting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole’s information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis. 1
On Quantum Coding for Ensembles of Mixed States
"... We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of ..."
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Cited by 21 (3 self)
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We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.
Information rates achievable with algebraic codes on quantum discrete memoryless channels
 IEEE Trans. Information Theory
, 2005
"... The highest information rate at which quantum errorcorrection schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to ..."
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Cited by 16 (7 self)
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The highest information rate at which quantum errorcorrection schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension, and the codes that are proven to have the desired performance are symplectic stabilizer codes. On the depolarizing channel, this work’s bound is actually the highest possible rate at which symplectic stabilizer codes work reliably.
Notes on the fidelity of symplectic quantum errorcorrecting codes
 International Journal on Quantum Information
, 2003
"... Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we shows that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the ‘probability ’ of the correctable errors for general quantum channels. The second observat ..."
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Cited by 16 (4 self)
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Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we shows that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the ‘probability ’ of the correctable errors for general quantum channels. The second observation states that for any coding rate below the quantum capacity, exponential convergence of the fidelity of some codes to unity is possible.
Quantum Feedback Channels
"... Abstract — In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory the nocloning theorem means that noiseless copying and feedback of quantum information cannot be achieved. In this paper, quantum feed ..."
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Cited by 11 (1 self)
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Abstract — In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory the nocloning theorem means that noiseless copying and feedback of quantum information cannot be achieved. In this paper, quantum feedback is defined as the unlimited use of a noiseless quantum channel from receiver to sender. Given such quantum feedback, it is shown to provide no increase in the entanglement–assisted capacities of a memoryless quantum channel, in direct analogy to the classical case. It is also shown that in various cases of nonassisted capacities, feedback may increase the capacity of memoryless quantum channels. Index Terms — Quantum information, channel capacity, quantum channels, entanglement, feedback.
The quantum capacity with symmetric side channels
, 2008
"... We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for highfidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels ..."
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Cited by 11 (3 self)
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We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for highfidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (oneway) channels, yielding one of the few entanglement measures that is monotonic under local operations with oneway classical communication (1LOCC), but not under the more general class of local operations with classical communication (LOCC).