Showing papers by "Charles H. Bennett published in 2001"

Remote State Preparation

Abstract: Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit--half that of teleportation--and even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.

Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

Abstract: The entanglement-assisted classical capacity of a noisy quantum channel is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that this capacity is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs $\rho$, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of $\rho$ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement assisted communication--communication over a discrete memoryless channel (DMC) between parties who share prior random information--we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMC's of equal capacity can simulate one another with unit asymptotic efficiency.

Quantum Information Processing

Abstract: : We have made progress on many fronts on the understanding and characterization of entanglement Various new forms of bound (ie undistillable) entanglement have been introduced, as part of our work on unextendable product states Cases of "superactivation" of bound entanglement, in which two different bound entangled states, when joined, produce distillable entanglement, have been established for fourparty states and have been conjectured for bipartite states These results show that the distillable entanglement is neither additive nor convex -- this achieves one of the major three year goals of this project An explicit formula for the entanglement of formation was found for all isotropic mixed states We discovered and characterized "remote state preparation", a generalization of quantum entanglement in which the transmitted quantum state is known to Alice Very recently, with A Winter, a new, more efficient protocol for RSP has been discovered We have continued to study many ideas for the simplification of the Kane approach to quantum computing, with the replacement of electron spin for nuclear spin Important simplifications over the currently published device designs will be possible We have worked out a scheme for the implementation of quantum computing, building on the theory of decoherence-free subspaces, that uses only the Heisenberg exchange interaction, or only the XY interaction We have provided detailed calculations of how g-factor engineering could be realized in III-V semiconductor heterostructures We have shown how to ameliorate the effects of spin orbit interaction in quantum-dot qubits We have begun master-equation modeling of superconducting qubits