Generalized remote state preparation: Trading cbits, qubits and ebits in quantum communication

Abstract

We consider the problem of communicating quantum states by simultaneously making use of a noiseless classical channel, a noiseless quantum channel and shared entanglement. We specifically study the version of the problem in which the sender is given knowledge of the state to be communicated. In this setting, a trade-off arises between the three resources, some portions of which have been investigated previously in the contexts of the quantum-classical trade-off in data compression, remote state preparation and superdense coding of quantum states, each of which amounts to allowing just two out of these three resources. We present a formula for the triple resource trade-off that reduces its calculation to evaluating the data compression trade-off formula. In the process, we also construct protocols achieving all the optimal points. These turn out to be achievable by trade-off coding and suitable time-sharing between optimal protocols for cases involving two resources out of the three mentioned above.

15 pages, 2 figures, 1 table

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• Remote Preparation of Single-Photon "Hybrid" Entangled and Vector-Polarization States
• Family of Concurrence Monotones and its Applications
• Continuous variable remote state preparation
• Entanglement-assisted communication of classical and quantum information
• Trade-off capacities of the quantum Hadamard channels
• Advances in quantum dense coding
• Applications of coherent classical communication and the Schur transform to quantum information theory
• Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
• Quantum Separability Criteria for Arbitrary Dimensional Multipartite States
• General criterion for oblivious remote state preparation
• Minimal classical communication and measurement complexity for quantum information splitting
• Derivation and experimental test of fidelity benchmarks for remote preparation of arbitrary qubit states
• Optimal superdense coding of entangled states
• Generalized Remote Preparation of Arbitrary $m$-qubit Entangled States via Genuine Entanglements
• Equivalence of Quantum States under Local Unitary Transformations
• Analysis of control power in controlled remote state preparation schemes
• Affinity-based measurement-induced nonlocality and its robustness against noise
• Controlled remote state preparation via partially entangled quantum channel
• Optimal joint remote state preparation of equatorial states
• Optimizing scheme of probabilistic remote preparation state