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.
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 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.
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter r and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter r.
Abstract The nonclassicality is the prerequisite for quantum states to be applied into quantum information, especially for quantum metrology. Here we theoretically investigate the non-classical properties of the non-Gaussian state generated by repeatedly operating a number-conserving generalized superposition of products (GSP), i.e., ( s 1 aa † + t 1 a † a ) m with s 1 2 + t 1 2 = 1 , on the squeezed thermal state (STS), in terms of second-order correlation function, Mandel’s Q parameter, quadrature squeezing and Wigner function (WF). It is shown that, compared to the cases of the STS, the GSP-STS with the high-order GSP operations ( m > 1) at the small-squeezing levels can be beneficial to the existence of the photon-antibunching effect, the sub-Poissonian distribution and the partial negativity of the WF, apart from the quadrature squeezing. In addition, for the case of m = 1, we also compare with the non-classical properties of several different non-Gaussian resources, involving the photon-subtracted-then-added (PSTA) STS, the GSP-STS and the photon-added-then-subtracted (PATS) STS. It is found that the PSTA-STS with respect to the sub-Poissonian distribution and the partial negativity of the WF has a better performance than others. Significantly, the generated GSP-STS has an obvious advantage of showing the photon-antibunching effects, compared to the PSTA-STS and the PATS-STS, which means that our scheme may have an excellent guidance for the practical implementations in quantum information.
The entanglement properties of non-Gaussian states are investigated, which are obtained by performing the photon addition, photon subtraction, photon-addition-then-subtraction, and photon-subtraction-then-addition operations on the two-mode squeezed vacuum state. We show that the partial von Neumann entropy of all the resulting states is greater than that of the original squeezed state, but only the photon-subtracted states and the photon-added-then-subtracted states have the stronger Einstein-Podolsky-Rosen correlation than the original squeezed state. Quantum teleportation of Braunstein and Kimble protocol is studied for coherent states, squeezed states, and mixed Gaussian states with the non-Gaussian entangled resources. For all the states to be teleported, the fidelity with the photon-subtracted and the photon-added-then-subtracted entangled resources is higher than that with the two-mode squeezed vacuum resource. Based on Bures fidelity, we find that quantum teleportation for mixed and classical single-mode Gaussian states is more faithful than for single-mode Gaussian states with high purity and nonclassicality.
Abstract We investigate the states generated in continuous variable (CV) optical fields by operating them with a number-conserving operator of the type , formed by the generalized superposition of products of field annihilation ( ) and creation ( ) operators, with . Such an operator is experimentally realizable and can be suitably manipulated to generate nonclassical optical states when applied on single- and two-mode coherent, thermal and squeezed input states. At low intensities, these nonclassical states can interact with a secondary mode via a linear optical device to generate two-mode discrete entangled states, which can serve as a resource in quantum information protocols. The advantage of these operations are tested by applying the generated entangled states as quantum channels in CV quantum teleportation, under the Braunstein and Kimble protocol. We observe that, under these operations, while the average fidelity of CV teleportation is enhanced for the nonclassical channel formed using input squeezed states, it remains at the classical threshold for input coherent and thermal states. This is due to the fact that though these operations can introduce discrete entanglement in all input states, it enhances the Einstein–Podolosky–Rosen correlations only in the nonclassical squeezed state inputs, leading to an advantage in CV teleportation. This shows that nonclassical optical states generated using the above operations on classical coherent and thermal state inputs are not useful for CV teleportation. This investigation could prove useful for the efficient implementation of noisy non-Gaussian channels, formed by linear operations, in future teleportation protocols.
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.