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Physical Review A

Conditional preparation of two-mode correlated photon number states of light

Xu‐Bo Zou, Yuli Dong, Guang‐Can Guo

Published Jul 11, 2006• 3 citations
Publisher

Abstract

We propose a scheme for conditional preparation of two-mode correlated photon number states of the form ${\ensuremath{\sum}}_{m=0}^{N}{C}_{m}\ensuremath{\mid}m{⟩}_{1}\ensuremath{\mid}m{⟩}_{2}$ by using linear optical elements and photon detectors. These states may find applications in testing Bell inequality based on quadrature using quadrature-phase homodyne measurement and optimize some quantum information processing protocols.

DOI
10.1103/physreva.74.015801

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We propose a scheme for conditional preparation of two-mode correlated photon number states of the form \ensuremath∑m=0NCm\ensuremath∣m⟩1\ensuremath∣m⟩2{\ensuremath{\sum}}_{m=0}^{N}{C}_{m}\ensuremath{\mid}m{⟩}_{1}\ensuremath{\mid}m{⟩}_{2}\ensuremath∑m=0N​Cm​\ensuremath∣m⟩1​\ensuremath∣m⟩2​ by using linear optical elements and photon detectors. These states may find applications in testing Bell inequality based on quadrature using quadrature-phase homodyne measurement and optimize some quantum information processing protocols.
We present a scheme that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. The state is near optimal for Bell-inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes a Gaussian entanglement distillation protocol and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter.
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We present an experimental scheme that realizes joint measurement of photon-number sum and phase-difference operators on a two-mode field. The proposed scheme only involves linear optical elements and photon detectors with single-photon sensitivity. Furthermore, we demonstrate that such a measurement setup can be applied to generate two-mode N-photon entangled states from a pair of squeezed vacuum states. These N-photon entangled states are useful resources for quantum-information processing, high-precision frequency measurement, and quantum optical lithography.
The measurement of quantum states of light is fundamental for the investigations of Quantum Optics and for the applications of Quantum Information. Here we present the implementation of a novel detection apparatus, that is a homodyne-like detection scheme based on photon-number-resolving detectors. Thanks to its hybrid nature, the apparatus is useful to investigate both the particle-like and wave-like properties of light. We tested the scheme in the measurement of the quadratures of different optical states, namely coherent states and mixtures of coherent states. In particular, we investigate the performance of our scheme compared to that of a standard homodyne detector.
Photon catalysis is a technique by which a readily available Gaussian state of light prepared in one mode is incident upon a beam splitter with a discrete number of photons, q, prepared in another mode; the resulting two-mode state is then subjected to single-photon resolving detection for q photons on one of the output modes. By employing beam splitters of different transmissivities and reflectivities, the subsequent single-mode state is shown to possess nonclassical properties such as quadrature squeezing and sub-Poissonian statistics. We consider the case in which the input state is the most general of pure single-mode Gaussian states: a squeezed coherent state. Noting the Gaussianity of the initial state, we demonstrate non-Gaussianity of the photon-catalyzed state by analyzing the quadrature uncertainty product and explicitly illustrate it through the Wigner quasi-probability distribution. We extend this technique to the two-mode squeezed states, whereby we perform photon catalysis on one mode of a two-mode squeezed vacuum state. The resulting correlated two-mode state may have applications in fundamental tests of quantum mechanics, such as violations of Bell’s inequalities, as the detection loophole can be closed due to the non-Gaussianity of the photon-catalyzed state. We also generalize our method to include state projective measurements for l≠q photons.