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Quantum entanglement
, 2007
"... Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laborat ..."
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Cited by 84 (1 self)
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Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laboratories as a new resource as real as energy.
The capacity of a quantum channel for simultaneous transmission of classical and quantum information
, 2008
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Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges
, 2010
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The mother of all protocols: restructuring quantum information’s family tree
 Proc. R. Soc. A
, 2009
"... 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 communicationassisted entanglem ..."
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Cited by 43 (15 self)
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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 communicationassisted 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 statemerging primitive of Horodecki, Oppenheim and Winter, a fully quantum reverse Shannon theorem, and a new class of distributed compression protocols for correlated quantum sources which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the socalled ‘father ’ protocol whose children provide the quantum capacity and the entanglementassisted capacity of a quantum channel, demonstrating that the division of singlesender/singlereceiver protocols into two families was unnecessary: all protocols in the family are children of the mother.
The structure of degradable quantum channels
, 2008
"... Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the struct ..."
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Cited by 17 (0 self)
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Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or antidegradable and present a complete description of antidegradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions (dB and dE respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with a environment that is “small ” in the sense dE ≤ dB. Such channels include
Quantum serial turbocodes
 IEEE Trans. Inf. Theory
"... Abstract — We present a theory of quantum serial turbocodes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding is free of 4 ..."
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Cited by 15 (3 self)
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Abstract — We present a theory of quantum serial turbocodes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding is free of 4cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code’s degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be noncatastrophic and nonrecursive. While the resulting families of turbocodes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases. I.
A father protocol for quantum broadcast channels
, 2006
"... We present a new protocol for quantum broadcast channels based on the fully quantum SlepianWolf protocol. The protocol yields an achievable rate region for entanglementassisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of Ma ..."
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Cited by 14 (3 self)
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We present a new protocol for quantum broadcast channels based on the fully quantum SlepianWolf protocol. The protocol yields an achievable rate region for entanglementassisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of Marton’s region for classical broadcast channels. The protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglementassisted classical communication. Regularized versions of all three rate regions are provably optimal.
The apex of the family tree of protocols: Optimal rates and resource inequalities
 New Journal of Physics
"... Abstract. We establish bounds on the maximum entanglement gain and minimum quantum communication cost of the Fully Quantum SlepianWolf protocol in the oneshot regime, which is considered to be at the apex of the existing family tree in Quantum Information Theory. These quantities, which are expres ..."
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Cited by 13 (4 self)
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Abstract. We establish bounds on the maximum entanglement gain and minimum quantum communication cost of the Fully Quantum SlepianWolf protocol in the oneshot regime, which is considered to be at the apex of the existing family tree in Quantum Information Theory. These quantities, which are expressed in terms of smooth min and maxentropies, reduce to the known rates of quantum communication cost and entanglement gain in the asymptotic i.i.d. scenario. We also provide an explicit proof of the optimality of these asymptotic rates. We introduce a resource inequality for the oneshot FQSW protocol, which in conjunction with our results, yields achievable oneshot rates of its children protocols. In particular, it yields bounds on the oneshot quantum capacity of a noisy channel in terms of a single entropic quantity, unlike previously bounds. We also obtain an explicit expression for the achievable rate for oneshot state redistribution. ar X iv