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New Journal of Physics

Engineering non-Gaussian entangled states with vortices by photon subtraction

G. S. Agarwal

Published Jul 7, 2011• 34 citations
Publisher

Abstract

We show how a quantum mechanical vortex state of a two-mode system can be generated from a squeezed vacuum by subtracting a photon. The vortex state has nonclassical properties; for example, its Wigner function can be negative, in contrast to the Wigner function of the two-mode squeezed vacuum. We show, by calculating the logarithmic negativity parameter, that the vortex state has stronger entanglement than the two-mode squeezed vacuum.

DOI
10.1088/1367-2630/13/7/073008

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We show how a quantum mechanical vortex state of a two-mode system can be generated from a squeezed vacuum by subtracting a photon. The vortex state has nonclassical properties; for example, its Wigner function can be negative, in contrast to the Wigner function of the two-mode squeezed vacuum. We show, by calculating the logarithmic negativity parameter, that the vortex state has stronger entanglement than the two-mode squeezed vacuum.
We investigate the entanglement patterns of photon-added and photon-subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the ``player'' modes, the others being ``spectators.'' We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast to the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state after photon subtraction can possess higher entanglement than that of the photon-added state, and we then compare it to that of the two-mode squeezed vacuum state. Moreover, we examine the non-Gaussianity of the photon-added and photon-subtracted states to find that the rich features provided by entanglement cannot be captured by the measure of nonclassicality.
In continuous-variable quantum information, non-Gaussian entangled states that are obtained from Gaussian entangled states via photon subtraction are known to contain more entanglement. This makes them better resources for quantum information processing protocols, such as, quantum teleportation. We discuss the teleportation of non-Gaussian, non-classical Schrödinger-cat states of light using two-mode squeezed vacuum light that is made non-Gaussian via subtraction of a photon from each of the two modes. We consider the experimentally realizable cat states produced by subtracting a photon from the single-mode squeezed vacuum state. We discuss two figures of merit for the teleportation process, (a) the fidelity, and (b) the maximum negativity of the Wigner function at the output. We elucidate how the non-Gaussian entangled resource lowers the requirements on the amount of squeezing necessary to achieve any given fidelity of teleportation, or to achieve negative values of the Wigner function at the output.
We study the production of entangled two- and N-mode quantum states of light in optical waveguides. To this end, we propose a quantum photonic circuit that produces a reconfigurable superposition of photon subtraction on two single-mode squeezed states. Under postselection, continuous variable or discrete variable entangled states with possibilities in quantum information processing are obtained. Likewise, nesting leads to higher-dimension entanglement with a similar design, enabling the generation of non-Gaussian continuous variable cluster states. Additionally, we show the operation of the device through the generation of quantum vortex states of light and propose an integrated device that measures their order and handedness. Finally, we study the non-Gaussianity, nonclassicality, and entanglement of the quantum states generated with this scheme by means of the optical field-strength distribution, Wigner function, and logarithmic negativity.
We introduce a kind of non-Gaussian entangled state, which can be obtained by operating a non-local coherent photon-subtraction operation on a two-mode squeezed vacuum. It is found that its normalization factor is only related to the Legendre polynomials, which is a compact expression. Its statistical properties are discussed by the negative region Wigner function with the analytical expression. As an application, the quantum teleportation for coherent states is considered by using the non-Gaussian state as an entangled channel. It is found that the teleportation fidelity can be enhanced by this non-Gaussian operation.
Nonclassicality of optical fields are the key resources in quantum information processing.Recently, Agarwal [New J. Phys., 13, 073008(2011)] proposed a method for engineering of a two-mode vortex state, a non-Gaussian state, by subtracting a photon from a two-mode squeezed state produced by down-converter from idler mode via a beam splitter with low reflectivity and detection of one photon by the avalanche photo diode (APD), or even better by a single-photon detector.We study the nonclassicalities of this state in terms of squeezing, antibunching, photon number correlation and distribution of photon number.In addition, we study higher-order nonclassical properties, viz., sum squeezing.We find that the non-Gaussian state shows strong nonclassical effects.