![]() ![]() Cambridge University Press, Cambridge (2013) Wilde, M.M.: Quantum Information Theory, 1st edn. Wilde, M.M., Krovi, H., Brun, T.A.: Coherent communication with continuous quantum variables. Harrow, A.: Coherent communication of classical messages. 70(13), 1895–1899 (1993)īennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. We develop the theory of \(\alpha \)-bits, including the applications above, and determine the \(\alpha \)-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants.īennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Changing \(\alpha \) interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. The size of the reference can be characterized by a parameter \(\alpha \) we call the associated resource an \(\alpha \)-bit. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. We study the effect of a constraint on the dimension of the reference system when considering information leakage. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. The source of these results is the theory of approximate quantum error correction. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. We identify a new communications resource, the zero-bit, which is precisely half the gap between them replacing classical bits by zero-bits makes teleportation asymptotically reversible. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. The structure of an α\documentclass.We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. We develop the theory of $\alpha$-bits, including the applications above, and determine the $\alpha$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. Changing $\alpha$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. The size of the reference can be characterized by a parameter $\alpha$ we call the associated resource an $\alpha$-bit. The decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. ![]() We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. ![]()
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