Connection between BosonSampling with quantum and classical input states.
Opt Express
; 28(5): 6929-6936, 2020 Mar 02.
Article
em En
| MEDLINE
| ID: mdl-32225930
ABSTRACT
BosonSampling is a problem of sampling events according to the transition probabilities of indistinguishable photons in a linear optical network. Computational hardness of BosonSampling depends on photon-number statistics of the input light. BosonSampling with multi-photon Fock states at the input is believed to be classically intractable but there exists an efficient classical algorithm for classical input states. In this paper, we present a mathematical connection between BosonSampling with quantum and classical light inputs. Specifically, we show that the generating function of a transition probability for Fock-state BosonSampling (FBS) can be expressed as a transition probability of thermal-light inputs. The closed-form expression of a thermal-light transition probability allows all possible transition probabilities of FBS to be obtained by calculating a single matrix permanent. Moreover, the transition probability of FBS is shown to be expressed as an integral involving a Gaussian function multiplied by a Laguerre polynomial, resulting in a fast oscillating integrand. Our work sheds new light on computational hardness of FBS by identifying the mathematical connection between BosonSampling with quantum and classical light.
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01-internacional
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MEDLINE
Idioma:
En
Revista:
Opt Express
Ano de publicação:
2020
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Article