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Sep 19, 2013
09/13

by
Igor Devetak; Toby Berger

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An upper bound on the low-entanglement remote state preparation (RSP) ebits vs. bits tradeoff curve (Bennett et al.,quant-ph/0006044) is found using techniques of classical information theory. We prove our coding scheme to be optimal amongst an important class of protocols, and conjecture the bound to be tight.

Source: http://arxiv.org/abs/quant-ph/0102123v3

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Sep 18, 2013
09/13

by
Hari Krovi; Igor Devetak

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Local pure states are an important resource for quantum computing. The problem of distilling local pure states from mixed ones can be cast in an information theoretic paradigm. The bipartite version of this problem where local purity must be distilled from an arbitrary quantum state shared between two parties, Alice and Bob, is closely related to the problem of separating quantum and classical correlations in the state and in particular, to a measure of classical correlations called the one-way...

Source: http://arxiv.org/abs/0705.4089v1

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Sep 20, 2013
09/13

by
Igor Devetak; Jon Yard

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With a statistical view towards information and noise, information theory derives ultimate limitations on information processing tasks. These limits are generally expressed in terms of entropic measures of information and correlations. Here we answer the quantum information-theoretic question: ``How correlated are two quantum systems from the perspective of a third?" by solving the following `quantum state redistribution' problem. Given an arbitrary quantum state of three systems, where...

Source: http://arxiv.org/abs/quant-ph/0612050v1

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Sep 18, 2013
09/13

by
Igor Devetak; Andreas Winter

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We study and solve the problem of distilling secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to achieve the "wire-tapper" bound, the difference of the mutual information Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way public communication. This result yields information--theoretic formulas for the distillable secret key, giving...

Source: http://arxiv.org/abs/quant-ph/0306078v1

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Sep 20, 2013
09/13

by
Zhicheng Luo; Igor Devetak

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The Shor-Preskill proof of the security of the BB84 quantum key distribution protocol relies on the theoretical existence of good classical error-correcting codes with the ``dual-containing'' property. A practical implementation of BB84 thus requires explicit and efficiently decodable constructions of such codes, which are not known. On the other hand, modern coding theory abounds with non-dual-containing codes with excellent performance and efficient decoding algorithms. We show that the...

Source: http://arxiv.org/abs/quant-ph/0608029v2

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Sep 18, 2013
09/13

by
Zhicheng Luo; Igor Devetak

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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 classical-quantum Slepian-Wolf 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...

Source: http://arxiv.org/abs/quant-ph/0611008v1

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Sep 22, 2013
09/13

by
Igor Devetak; Toby Berger

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We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an unrestricted classical side channel, we find the exact quantum rate-distortion function for a source of isotropic qubits. An upper bound we believe to be exact is found in the case of biased sources. We establish that in this scenario optimal rate-distortion codes...

Source: http://arxiv.org/abs/quant-ph/0011085v3

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Sep 21, 2013
09/13

by
Konrad Banaszek; Igor Devetak

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We calculate the trade-off between the quality of estimating the quantum state of an ensemble of identically prepared qubits and the minimum level of disturbance that has to be introduced by this procedure in quantum mechanics. The trade-off is quantified using two mean fidelities: the operation fidelity which characterizes the average resemblance of the final qubit state to the initial one, and the estimation fidelity describing the quality of the obtained estimate. We analyze properties of...

Source: http://arxiv.org/abs/quant-ph/0104008v2

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Sep 21, 2013
09/13

by
Jon Yard; Igor Devetak

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Consider many instances of an arbitrary quadripartite pure state of four quantum systems ACBR. Alice holds the AC part of each state, Bob holds B, while R represents all other parties correlated with ACB. Alice is required to redistribute the C systems to Bob while asymptotically retaining the purity of the global states. We prove that this is possible using Q qubits of communication and E ebits of shared entanglement between Alice and Bob provided that Q < I(R;C|B)/2 and Q + E < H(C|B)....

Source: http://arxiv.org/abs/0706.2907v1

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Sep 22, 2013
09/13

by
Igor Devetak; Andreas Winter

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We describe how to achieve optimal entanglement generation and one-way entanglement distillation rates by coherent implementation of a class of secret key generation and secret key distillation protocols, respectively. This short paper is a high-level descrioption of our detailed papers [8] and [10].

Source: http://arxiv.org/abs/quant-ph/0307053v1

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Sep 23, 2013
09/13

by
Garry Bowen; Igor Devetak; Stefano Mancini

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The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real world communication channels experience noise which is modelled better by errors that are correlated between separate channel uses. In this paper, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of...

Source: http://arxiv.org/abs/quant-ph/0312216v2

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Sep 21, 2013
09/13

by
Jon Yard; Igor Devetak; Patrick Hayden

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We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region characterizes the rates at which it is possible for one sender to send classical information while the other sends quantum information. The second region gives the rates at which each sender can send quantum information. We give an example of a channel for which each region has a single-letter...

Source: http://arxiv.org/abs/cs/0508031v1

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Sep 22, 2013
09/13

by
Jon Yard; Igor Devetak; Patrick Hayden

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We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional 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. For each region, we give an example of a channel for which the...

Source: http://arxiv.org/abs/quant-ph/0501045v3

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Sep 22, 2013
09/13

by
Jon Yard; Patrick Hayden; Igor Devetak

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We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions...

Source: http://arxiv.org/abs/quant-ph/0603098v2

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Sep 19, 2013
09/13

by
Min-Hsiu Hsieh; Igor Devetak; Todd Brun

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Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these...

Source: http://arxiv.org/abs/0708.2142v1

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Sep 19, 2013
09/13

by
Todd Brun; Igor Devetak; Min-Hsiu Hsieh

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We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error correcting codes, thus allowing us to ``quantize'' all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound...

Source: http://arxiv.org/abs/quant-ph/0610092v1

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Sep 23, 2013
09/13

by
Min-Hsiu Hsieh; Igor Devetak; Andreas Winter

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We find a regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple access channels (QMAC). We illustrate the capacity region calculation with the example of the collective phase-flip channel which admits a single-letter characterization. On the way, we provide a first-principles proof of the EA coding theorem based on a packing argument. We observe that the Holevo-Schumacher-Westmoreland theorem may be obtained from a modification of our EA protocol. We remark...

Source: http://arxiv.org/abs/quant-ph/0511228v2

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Sep 20, 2013
09/13

by
Todd Brun; Igor Devetak; Min-Hsiu Hsieh

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We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional stabilizer codes are equivalent to dual-containing symplectic codes. In contrast, EAQEC codes do not require the dual-containing condition, which greatly simplifies their construction. We show how any quaternary classical code can be made into a EAQEC code. In...

Source: http://arxiv.org/abs/quant-ph/0608027v2

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Sep 18, 2013
09/13

by
Min-Hsiu Hsieh; Todd A. Brun; Igor Devetak

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We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Shor-Steane (CSS) construction do not need to satisfy the dual-containing property as long as pre-shared entanglement is available to both sender and receiver. We can use this to avoid the many 4-cycles which typically arise in dual-containing LDPC codes. The...

Source: http://arxiv.org/abs/0803.0100v2

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Sep 18, 2013
09/13

by
Anura Abeyesinghe; Igor Devetak; Patrick Hayden; Andreas Winter

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We give a simple, direct proof of the "mother" protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian-Wolf protocol, simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of...

Source: http://arxiv.org/abs/quant-ph/0606225v1

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Sep 20, 2013
09/13

by
Igor Devetak; Marius Junge; Christopher King; Mary Beth Ruskai

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We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi > < psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an...

Source: http://arxiv.org/abs/quant-ph/0506196v2

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Jul 20, 2013
07/13

by
Charles H. Bennett; Igor Devetak; Peter W. Shor; John A. Smolin

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We exhibit discrete memoryless quantum channels whose quantum capacity assisted by two-way classical communication, $Q_2$, exceeds their unassisted one-shot Holevo capacity $C_H$. These channels may be thought of as having a data input and output, along with a control input that partly influences, and a control output that partly reveals, which of a set of unitary evolutions the data undergoes en route from input to output. The channel is designed so that the data's evolution can be exactly...

Source: http://arxiv.org/abs/quant-ph/0406086v1

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Sep 17, 2013
09/13

by
Charles H. Bennett; Igor Devetak; Aram W. Harrow; Peter W. Shor; Andreas Winter

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Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the use of one noisy channel to simulate another. For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. In the classical case, shared randomness...

Source: http://arxiv.org/abs/0912.5537v2