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International Conference on Quantum Information

Coherent States Engineering with Linear Optics

Bing He, János A. Bergou

Published Jan 1, 2008• 0 citations
Publisher

Abstract

We present a general linear optics based approach to implement contractive transformations that map products of N coherent states to products of M coherent states (M ≤ N) and apply it to nondestructive quantum database search.
DOI
10.1364/icqi.2008.jmb65

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The general transformation of the product of coherent states ${\ensuremath{\prod}}_{i=1}^{N}|{\ensuremath{\alpha}}_{i}⟩$ to the output state ${\ensuremath{\prod}}_{i=1}^{M}|{\ensuremath{\beta}}_{i}⟩$ (N=MN=MN=M or $N\ensuremath{\ne}M$), which is realizable with linear optical circuit, is characterized with a linear map from the vector $({\ensuremath{\alpha}}_{1}^{\ensuremath{\ast}},\dots{},{\ensuremath{\alpha}}_{N}^{\ensuremath{\ast}})$ to $({\ensuremath{\beta}}_{1}^{\ensuremath{\ast}},\dots{},{\ensuremath{\beta}}_{M}^{\ensuremath{\ast}})$. A correspondence between the transformations of a product of coherent states and those of a single photon state is established with such linear maps. It is convenient to apply this linear transformation method to design any linear optical scheme working with coherent states. The examples include message encoding and quantum database searching. The limitation of manipulating entangled coherent states with linear optics is also discussed.
We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in a superposition of optical modes, linear optics transformations and measurements with single-photon threshold detectors. This provides a general framework for transforming a wide class of protocols in quantum communication into a form in which they can be implemented with current technology. In particular, we apply the mapping to quantum communication complexity, providing general conditions under which quantum protocols can be implemented with coherent states and linear optics while retaining exponential separations in communication complexity compared to the classical case. Finally, we make use of our results to construct a protocol for the Hidden Matching problem that retains the known exponential gap between quantum and classical one-way communication complexity.