Entanglement improvement via a quantum scissor in a realistic environment

We propose a protocol for improving quantum entanglement based on a quantum scissor scheme [D. T. Pegg et al., Phys. Rev. Lett. 81, 1604 (1998)]. Compared to existing protocols for entanglement improvement, our scheme does not require biside operation on two-mode squeezed vacuum states. This greatly enhances the success probability as well as entanglement, while reducing the resources. A squared gain factor can be obtained from our scheme. In addition, our scheme is robust against the decoherence when considering more realistic cases. Finally, a comparison between the single-side quantum scissor scheme and the single-side quantum catalysis is also investigated.

Figure 1

Quantum scissors scheme for any input state ${\rho }_{\mathrm{in}}$. The effect will convert any input state into an output state in a Fock space spanned by both a vacuum and single photon. The beam splitters (${\mathrm{BS}}_{ac}$ and ${\mathrm{BS}}_{bc}$) are asymmetrical with transmission coefficient $T_{ac}$ and $T_{bc}$, respectively. The relation between the output and input states can be described by an operator $M_{ab}$.

Figure 2

Scheme of quantum scissors device (QSD) for the TMSV (a) single-side scheme and (b) biside scheme. The relation between input and output can be described by the operator $M_{ab}$ and $M_{a^{\prime }{b}^{\prime }}$.

Figure 3

The logarithmic negativity is plotted as a function of the transmissivity $T_{ac}$ and the squeezing parameter $r$ for given (a) $T_{ac}=0.5$ and (b) $T_{ac}=T_{bc},$ respectively. The corresponding success probability is shown in (c) and (d). Here, for comparison, the corresponding logarithmic negativity of the TMSV is also plotted (see the dotted line).

Figure 4

The difference of logarithmic negativity between the generated state and the TMSVS is plotted as a function of the transmissivity $T_{ac}$ and $T_{bc}$ for the given squeezing parameter (a) $r=0.1$ and (b) $r=0.2,$ respectively.

Figure 5

Scheme of the QSD for the realistic TMSV (a) single-side case and (b) biside case. The relation between output and input can be described by operator $M_{ab}$ and $M_{a^{\prime }{b}^{\prime }}$.

Figure 6

The logarithmic negativity is plotted as a function of squeezing parameter $r$ for given transmissivity $T$ and dissipative ${\eta }_t$: (a) ${\eta }_t=0.90$ and $T=0.92,0.82$, and (b) $T=0.92,{\eta }_t=0.9,0.85$, respectively. The corresponding logarithmic negativity of the TMSV is also plotted (see black dotted line).

Figure 7

The logarithmic negativity is plotted as a function of squeezing parameter $r$ for given transmissivity $T=0.92$ and dissipative ${\eta }_t=0.90,0.88$ for (a) the entanglement rate $E_r$ and (b) the enhancement rate of entanglement $\mathrm{\Delta }{E}_r,$ respectively.

Figure 8

Realistic scheme of a single-side QSD for any input state ${\rho }_{\mathrm{in}}$. The beam splitters (${\mathrm{BS}}_{ac}$ and ${\mathrm{BS}}_{bc}$) are asymmetrical with transmission coefficients $T_{ac}$ and $T_{bc}$, respectively. The relation between output and input can be described by operator ${\widehat{M}}_S$. And the heralded single photon is generated from the two-mode squeezed state $\left|\mathrm{\Psi }\right.〉$. Here, all detectors are dichotic “on-off” detectors.

Figure 9

The entanglement degree and success probability as a function of squeezing parameter $r$ and transmission efficiency $T$, for ${\eta }_t=0.9,\lambda =0.2$, and (a),(b) $T=0.92$, and (c),(d) $r=0.2.$

Figure 10

The entanglement of the output state (a) after QSD and (b) after catalysis, as a function of transmission for several given squeezing parameters $r=0.1,0.2$ and ${\eta }_t=0.9$. Single-side QSD: black and blue; two-side QSD: red and orange. For comparison, the entanglement of the TMSVS is also plotted in dashed blue and dashed pink for $r=0.1,0.2$, respectively. (c) Success probability as a function of (c) $r$ for given $T$, and (d) $T$ for given $r$ with ${\eta }_t=0.9$.