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Journal of the Optical Society of America B

Enhanced Bell violation by a coherent superposition of photon subtraction and addition

Jiyong Park, Su-Yong Lee, Hai-Woong Lee, Hyunchul Nha

Published Apr 5, 2012• 30 citations
Publisher

Abstract

We show that the coherent superposition ta^+ra^† of photon subtraction and addition applied to each local mode of a two-mode entangled state can enhance the nonlocality manifested by the violation of a Bell inequality. A two-mode squeezed state is used as an input state for this demonstration with four different Bell inequalities employed: Bell inequalities adopting displaced parity operator, pseudospin operator, homodyne measurement, and conditional entropy, respectively. We find that the coherent operation significantly enhances the nonlocality remarkably in the weak squeezing limit, compared with other possible non-Gaussian operations. It can also give a maximal Bell violation with a very small squeezing for the inequalities with pseudospin operator and conditional entropy.

DOI
10.1364/josab.29.000906

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We show that the coherent superposition ta^+ra^† of photon subtraction and addition applied to each local mode of a two-mode entangled state can enhance the nonlocality manifested by the violation of a Bell inequality. A two-mode squeezed state is used as an input state for this demonstration with four different Bell inequalities employed: Bell inequalities adopting displaced parity operator, pseudospin operator, homodyne measurement, and conditional entropy, respectively. We find that the coherent operation significantly enhances the nonlocality remarkably in the weak squeezing limit, compared with other possible non-Gaussian operations. It can also give a maximal Bell violation with a very small squeezing for the inequalities with pseudospin operator and conditional entropy.
Violation of Bell inequality is a prominent detection method for quantum correlations present in composite quantum systems, both in finite and infinite dimensions. We investigate the consequence of the violation of local realism based on pseduospin operators when photons are added or subtracted in a single mode or in both the modes of the two-mode squeezed states of light in the presence of noise. In the noiseless situation, we show that for addition (subtraction) of photons in a single mode, there is an overall enhancement in the maximal violation, although we observe an interplay between monotonicity and nonmonotonicity in the violation of Bell inequality depending on the squeezing strength. Moreover, we report that for low squeezing or low number of photons added or subtracted, subtraction in both the modes can lead to higher violation of local realism than that in the case of addition. For any choice of parameters, such ordering is not seen if one compares their entanglement contents. In the event of a faulty twin-beam generator, we obtain a lower than expected squeezing in the state. In such a case, or in imperfect photon addition (subtraction) or under local noise, we find that the violation of local realism by the noise-affected two-mode squeezed states always decreases. Interestingly, however, we notice that photon addition (subtraction) can in general help to conquer the ill effects of noise by enhancing the violation of local realism or by transforming nonviolating states to violating ones, thereby acting as an activating agent.
We study how conditional photon operations can affect multipartite quantum correlations, specifically nonlocality and entanglement, of the continuous-variable Greenberger-Horne-Zeilinger (GHZ) states. We find that the violation of the Mermin-Klyshko inequality revealing the multipartite nonlocality can be made stronger with photon subtraction applied on each mode of the original GHZ states, particularly in a weak squeezing regime. Photon addition applied on local modes also turns out to enhance the degree of multipartite nonlocality in a broad range of parameters. We further investigate the effects of the photon operations on the degree of multipartite entanglement by looking into the Gaussian tangle, the fidelity of teleportation network, and the quadrature correlations. We find that photon subtraction applied on two modes enhances those entanglement characteristics in a practical squeezing regime while there is no improvement made by photon addition.
We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation $t\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}+r{\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}$ of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the Einstein-Podolsky-Rosen--type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$ and the addition ${\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}$ particularly in the small-squeezing regime, whereas the optimal operation becomes the photon subtraction (case of r=0r=0r=0) in the large-squeezing regime.
A new entangled quantum state is introduced by applying local coherent superposition (CS) (ra†+ta) of photon subtraction and addition to each mode of an even entangled coherent state (EECS). The properties of entanglement are investigated in terms of the Einstein–Podolsky–Rosen (EPR) correlation, the degree of entanglement, and the average fidelity of quantum teleportation. It is found that single- and two-mode CS operations can improve the EPR correlation of the EECS in a big (>0.88) and small (<0.52) region of amplitude, respectively. The enhanced entanglement and fidelity depend on the even or odd order of CS. All optimal results are not achieved at two extreme cases of t=0, 1.
A new entangled quantum state is introduced by applying local coherent superposition (ra^+ +ta) of photon subtraction and addition to each mode of even entangled coherent state (EECS) and the properties of entanglement are investigated. It is found that the Shchukin-Vogel inseparability, the degree of entanglement and the average fidelity of quantum teleportation of the EECS can be improved due to the coherent superposition operation. The effects of improvement by coherent superposition operation are better than those by single (a^+) and two-photon (a^+ b^+) addition operations under a small region of amplitude.
We analyze effects of squeezing upon superpositions of coherent states (SCSs) and entangled coherent states for Bell-inequality tests. We find that external squeezing can always increase the degrees of Bell violations, if the squeezing direction is properly chosen, for the case of photon parity measurements. On the other hand, when photon on/off measurements are used, the squeezing operation can enhance the degree of Bell violations only for moderate values of amplitudes and squeezing. We point out that a significant improvement is required over currently available squeezed SCSs in order to directly demonstrate a Bell-inequality violation in a real experiment.