A Communication-Efficient Nonlocal Measurement With Application to Communication Complexity and Bipartite Gate Capacities

Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising properties: 1) simulating it with the assistance of unlimited EPR...

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Bibliographic Details
Published in:IEEE transactions on information theory 2011-08, Vol.57 (8), p.5504-5508
Main Authors: Harrow, A. W., Leung, D. W.
Format: Article
Language:English
Subjects:
Access methods and protocols, osi model
Accuracy
Applied sciences
Classical and quantum physics: mechanics and fields
Communication capacity
Communication channels
communication complexity
Complement
Complexity theory
Computer simulation
Entangled states
Entanglement
entanglement capacity
entanglement spread
Exact sciences and technology
Gates
Information theory
Information, signal and communications theory
Logic gates
Measurement
Mutual information
Physics
Protocols
Quantum entanglement
Quantum information
quantum Shannon theory
Registers
Simulation
Tasks
Telecommunications
Telecommunications and information theory
Teleprocessing networks. Isdn
unitary gates
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Summary:Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising properties: 1) simulating it with the assistance of unlimited EPR pairs requires far more communication than with a better choice of entangled state, and 2) its communication capacity is far lower than its capacity to create entanglement. This suggests that 1) unlimited EPR pairs are not the most general model of entanglement assistance for two-party communication tasks, and 2) the entangling and communicating abilities of a unitary interaction can vary nearly independently. The technical contribution behind these results is a communication-efficient protocol for measuring whether an unknown shared state lies in a specified rank-one subspace or its orthogonal complement.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2158468