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18
A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
, 2013
"... We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using socalled oneshot entropies. These characterizations — in contrast ..."
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Cited by 26 (15 self)
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We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using socalled oneshot entropies. These characterizations — in contrast to earlier results — enable us to derive tight second order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The oneshot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree (up to logarithmic terms) with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our technique also naturally yields bounds on operational quantities for finite block lengths.
Distilling common randomness from bipartite quantum states
, 2008
"... The problem of converting noisy quantum correlations between two parties into noiseless classical ones using a limited amount of oneway classical communication is addressed. A singleletter formula for the optimal tradeoff between the extracted common randomness and classical communication rate is ..."
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Cited by 18 (8 self)
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The problem of converting noisy quantum correlations between two parties into noiseless classical ones using a limited amount of oneway classical communication is addressed. A singleletter formula for the optimal tradeoff between the extracted common randomness and classical communication rate is obtained for the special case of classicalquantum correlations. The resulting curve is intimately related to the quantum compression with classical side information tradeoff curve Q ∗ (R) of Hayden, Jozsa and Winter. For a general initial state we obtain a similar result, with a singleletter formula, when we impose a tensor product restriction on the measurements performed by the sender; without this restriction the tradeoff is given by the regularization of this function. Of particular interest is a quantity we call “distillable common randomness ” of a state: the maximum overhead of the common randomness over the oneway classical communication if the latter is unbounded. It is an operational measure of (total) correlation in a quantum state. For classicalquantum correlations it is given by the Holevo mutual information of its associated ensemble, for pure states it is the entropy of entanglement. In general, it is given by an optimization problem over measurements and regularization; for the case of separable states we show that this can be singleletterized.
Channel simulation with quantum side information
, 2006
"... We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classicalquantum SlepianWolf problem. The optimal noiseless communication rate is found to be reduced from t ..."
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Cited by 15 (1 self)
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We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classicalquantum SlepianWolf problem. The optimal noiseless communication rate is found to be reduced from the mutual information between the channel input and output by the Holevo information between the channel output and the quantum side information. Our main theorem has two important corollaries. The first is a quantum generalization of the WynerZiv problem: ratedistortion theory with quantum side information. The second is an alternative proof of the tradeoff between classical communication and common randomness distilled from a quantum state. The fully quantum generalization of the problem considered is quantum state redistribution. Here the sender and receiver share a mixed quantum state and the sender wants to transfer part of her state to the receiver using entanglement and quantum communication. We present outer and inner bounds on the achievable rate pairs. 1
Capacity theorems for quantum multiple access channels,” submitted to
 IEEE Intern. Symp. Info. Th
, 2005
"... We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multiletter characterizations of two different twodimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, wh ..."
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Cited by 14 (4 self)
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We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multiletter characterizations of two different twodimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. We give an example of a channel with a singleletter classicalquantum region. We conclude with connections to other work and a conjecture on a generalization where each user simultaneously sends classical and quantum information. 1
Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
, 2009
"... We give optimal tradeoffs between classical communication, quantum communication, and entanglement for processing information in the Shannontheoretic setting. We first prove a “unitresource” capacity theorem that applies to the scenario where only the above three noiseless resources are available ..."
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Cited by 11 (8 self)
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We give optimal tradeoffs between classical communication, quantum communication, and entanglement for processing information in the Shannontheoretic setting. We first prove a “unitresource” capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three fundamental protocols of teleportation, superdense coding, and entanglement distribution. Furthermore, no protocol other than these three fundamental ones is necessary to generate the unit resource capacity region. We then prove the “direct static ” capacity theorem that applies to the scenario where a large number of copies of a noisy bipartite state are available (in addition to consumption or generation of the above three noiseless resources). The result is that a coding strategy involving the classicallyassisted mother protocol and the three fundamental protocols is optimal. We finally prove the “direct dynamic” capacity theorem. This theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources. The optimal strategy combines the classicallyenhanced father protocol with the three fundamental unit protocols. Interestingly, one octant of the directdynamic capacity region applies to an open question concerning the use of entanglementassisted coding and teleportation for entanglement and classicallyassisted quantum communication. PACS numbers: 03.67.Hk, 03.67.Pp
OneShot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys
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On the distributed compression of quantum information
 IEEE Trans. Inf. Theory
, 2004
"... Abstract—The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlat ..."
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Cited by 7 (2 self)
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Abstract—The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian–Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including informationdisturbance questions, entanglement distillation and quantum error correction. Index Terms—Compression, distributed, quantum information, Slepian–Wolf. I.
On the power of twoparty quantum cryptography
, 2009
"... We study quantum protocols among two distrustful parties. Under the sole assumption of correctness—guaranteeing that honest players obtain their correct outcomes—we show that every protocol implementing a nontrivial primitive necessarily leaks information to a dishonest player. This extends known i ..."
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Cited by 6 (2 self)
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We study quantum protocols among two distrustful parties. Under the sole assumption of correctness—guaranteeing that honest players obtain their correct outcomes—we show that every protocol implementing a nontrivial primitive necessarily leaks information to a dishonest player. This extends known impossibility results to all nontrivial primitives. We provide a framework for quantifying this leakage and argue that leakage is a good measure for the privacy provided to the players by a given protocol. Our framework also covers the case where the two players are helped by a trusted third party. We show that despite the help of a trusted third party, the players cannot amplify the cryptographic power of any primitive. All our results hold even against quantum honestbutcurious adversaries who honestly follow the protocol but purify their actions and apply a different measurement at the end of the protocol. As concrete examples, we establish lower bounds on the leakage of standard universal twoparty primitives such as oblivious transfer.