Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication

Abstract

Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain times and locations, and a representation of bipartite unitaries based on a group Fourier transform.

Minor corrections so as to agree with the published version

References in corpus (10)

• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Parallelism for Quantum Computation with Qudits
• Communication Links for Distributed Quantum Computation
• Separable Operations on Pure States
• On the efficiency of nonlocal gates generation
• Local implementation of nonlocal operations of block forms
• Types of quantum information
• Quantum entanglement in states generated by bilocal group algebras
• Implementation of multipartite unitary operations with limited resources
• Optimizing local protocols implementing nonlocal quantum gates

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• A quantum homomorphic encryption scheme for polynomial-sized circuits
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• Separable Operations, Graph Codes and the Location of Quantum Information