A scheme for improving entanglement is proposed by repeatedly performing number-conserving generalized superposition of products (GSP) operation, i.e., (saa†+ta†a)m with s²+t²=1, on each modes of even entangled coherent state (EECS). Both Einstein-Podolsky-Rosen (EPR) correlation and concurrence are used as the measures for describing entanglement. It is found that both single-mode and two-mode-symmetric GSP operations can be used for the entanglement improvement. In particular, for the optimal EPR correlation, the GSP-EECS with two-mode-symmetric first-order operations presents a better performance for the entanglement improvement than the cases of high-order GSP operations. Compared to several special non-Gaussian operations, including photon subtraction-then-addition (PSTA) (s=0) and photon-addition-then-subtraction (PATS) (s=1), it is shown that the entanglement of GSP-EECS is always superior to those of both PSTA-EECS and PATS-EECS at a small amplitude level. When the GSP-EECS is used as the entangled resource for teleportation, our optimal teleportation fidelity presents the best performance.
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.
Abstract The non-Gaussian operation, which can be easily implemented by current techniques, is an effective way for the improvement of the continuous-variable entanglement. Here, we theoretically propose a scheme for generating a number-conserving two-mode generalized superposition of products (TM-GSP) state by performing the -order GSP operations i.e. on an input two-mode squeezed vacuum (TMSV) state. Then, the entanglement properties of the TM-GSP state are analyzed detailedly by means of logarithmic negative, Einstein–Podolsky–Rosen (EPR) correlation and two-mode squeezing property. It is shown that, in contrast to the TMSV case, for the optimal choices of s 1 and s 2 , the entanglement properties of the TM-GSP state can be improved by using symmetric GSP operations ( ) and single-side GSP operations . Furthermore, the fidelity effect is also considered when the TM-GSP state is used as the entangled resource under the Braunstein and Kimble scheme. In terms of the optimal teleportation fidelity, it is found that the effect of the single GSP operation is equivalent to that of the case . This phenomenon also exists in logarithmic negative, EPR correlation and two-mode squeezing property. These results show that the prepared TM-GSP state may provide a well application in the fields of quantum information processing.
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 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=0) in the large-squeezing regime.
We propose a theoretical scheme to improve the resolution and precision of phase measurement with parity detection by using a nonclassical state generated by applying a number-conserving generalized superposition of products (GSP) operation, ${\left(sa{a}^{\ifmmode\dagger\else\textdagger\fi{}}+t{a}^{\ifmmode\dagger\else\textdagger\fi{}}a\right)}^{m}$ with
s2+t2=1, on a two-mode squeezed vacuum (TMSV) state as the input of Mach-Zehnder interferometer. Then, the statistical properties of the proposed GSP-TMSV are investigated via average photon number (APN), antibunching effect, and two-mode squeezing. Particularly, both higher order
m GSP operation and lower proportion parameter
s are beneficial for presenting larger total APN, which leads to the improvement of quantum Fisher information (QFI). In addition, we also compare the phase measurement precisions with and without photon losses between our scheme and the previous photon subtraction or photon addition schemes. It is found that our scheme, especially for the case of
s=0, even in the presence of photon losses, has the best performance via the enhanced phase resolution, sensitivity, and QFI when compared to those previous schemes. Interestingly, without losses, the standard quantum-noise limit (SQL) is always broken through for our scheme and the phase uncertainty associated with the state of our scheme is closer to the corresponding Heisenberg limit (HL) than the TMSV in the larger total APN region, especially for the case of two-side GSP operation $\left(m,n\right)\ensuremath{\in}\left(1,1\right)$. However, in the presence of photon losses, the HL cannot be beaten, but the SQL can be broken through, particularly for the large total APN regimes.
Single-photon-level non-Gaussian operations—photon addition, photon subtraction, and their coherent superposition—are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define 'entanglement enhancement rate' as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.