%0 Journal Article
%J International Journal of Quantum Information
%D 2006
%T Two-way quantum communication channels
%A Andrew M. Childs
%A Debbie W. Leung
%A Hoi-Kwong Lo
%X We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel.
%B International Journal of Quantum Information
%V 04
%P 63 - 83
%8 2006/02/01
%G eng
%U http://arxiv.org/abs/quant-ph/0506039v1
%N 01
%! Int. J. Quanum Inform.
%R 10.1142/S0219749906001621
%0 Journal Article
%J Physical Review A
%D 2005
%T Unified derivations of measurement-based schemes for quantum computation
%A Andrew M. Childs
%A Debbie W. Leung
%A Michael A. Nielsen
%X We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308, 96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes.
%B Physical Review A
%V 71
%8 2005/3/17
%G eng
%U http://arxiv.org/abs/quant-ph/0404132v2
%N 3
%! Phys. Rev. A
%R 10.1103/PhysRevA.71.032318
%0 Journal Article
%J IEEE Transactions on Information Theory
%D 2004
%T Reversible simulation of bipartite product Hamiltonians
%A Andrew M. Childs
%A Debbie W. Leung
%A Guifre Vidal
%X Consider two quantum systems A and B interacting according to a product Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used to simulate each other reversibly (i.e., without efficiency losses) with the help of local unitary operations and local ancillas. Accordingly, all non-local features of a product Hamiltonian -- including the rate at which it can be used to produce entanglement, transmit classical or quantum information, or simulate other Hamiltonians -- depend only upon a single parameter. We identify this parameter and use it to obtain an explicit expression for the entanglement capacity of all product Hamiltonians. Finally, we show how the notion of simulation leads to a natural formulation of measures of the strength of a nonlocal Hamiltonian.
%B IEEE Transactions on Information Theory
%V 50
%P 1189 - 1197
%8 2004/06/01
%G eng
%U http://arxiv.org/abs/quant-ph/0303097v1
%N 6
%! IEEE Trans. Inform. Theory
%R 10.1109/TIT.2004.828069
%0 Journal Article
%J Physical Review A
%D 2001
%T Realization of quantum process tomography in NMR
%A Andrew M. Childs
%A Isaac L. Chuang
%A Debbie W. Leung
%X Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.
%B Physical Review A
%V 64
%8 2001/6/13
%G eng
%U http://arxiv.org/abs/quant-ph/0012032v1
%N 1
%! Phys. Rev. A
%R 10.1103/PhysRevA.64.012314
%0 Journal Article
%J Physical Review A
%D 2001
%T Universal simulation of Markovian quantum dynamics
%A Dave Bacon
%A Andrew M. Childs
%A Isaac L. Chuang
%A Julia Kempe
%A Debbie W. Leung
%A Xinlan Zhou
%X Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators) corresponding to the dynamics of open quantum systems. We propose a framework for the generation of Markovian quantum dynamics and study the resources needed for universality. For the case of a single qubit, we show that a single nonunitary process is necessary and sufficient to generate all unital Markovian quantum dynamics, whereas a set of processes parametrized by one continuous parameter is needed in general. We also obtain preliminary results for the unital case in higher dimensions.
%B Physical Review A
%V 64
%8 2001/11/9
%G eng
%U http://arxiv.org/abs/quant-ph/0008070v2
%N 6
%! Phys. Rev. A
%R 10.1103/PhysRevA.64.062302