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Chinese Journal of Physics

Enhancing quantum entanglement with the local displacement-based quantum scissor

Ying Xia, Yaxin Wang, Tianqi Xiao, Wei Ye, Zeyang Liao, Xiaoqi Zhou

Published Feb 26, 2025• 2 citations

Abstract

Entangled quantum states serve as a pivotal resource in quantum information processing, where the preparation of highly entangled quantum states is a core issue. In this paper, we propose a local displacement-based quantum scissor (LDQS) scheme to enhance the entanglement of the two-mode squeezed vacuum (TMSV) state. By introducing a local displacement operation in the traditional quantum scissor, the entanglement of the TMSV state is enhanced by approximately 75 % for low initial squeezing ( r = 0 . 2 ) conditions. Compared with the local squeezing-based quantum scissor scheme (Liu et al., 2022), the LDQS scheme eliminates the need for additional pumping and the use of inefficient nonlinear crystals, thereby simplifying the experimental procedure. Moreover, the LDQS scheme provides a greater enhancement in entanglement when both schemes are implemented with the same success probability. Finally, we also demonstrate that the LDQS operation can be used to enhance the entanglement of the TMSV state in lossy channels. These advantages suggest that our scheme shows promise for application in various quantum information tasks, including quantum metrology and quantum communication. • Enhancing entanglement with local displacement-based quantum scissor scheme. • The scheme is easier to implement than the local squeezing-based quantum scissor. • The scheme exhibits robustness against entanglement degradation.

DOI: 10.1016/j.cjph.2025.02.025

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Entangled quantum states serve as a pivotal resource in quantum information processing, where the preparation of highly entangled quantum states is a core issue. In this paper, we propose a local displacement-based quantum scissor (LDQS) scheme to enhance the entanglement of the two-mode squeezed vacuum (TMSV) state. By introducing a local displacement operation in the traditional quantum scissor, the entanglement of the TMSV state is enhanced by approximately 75 % for low initial squeezing ( r = 0 . 2 ) conditions. Compared with the local squeezing-based quantum scissor scheme (Liu et al., 2022), the LDQS scheme eliminates the need for additional pumping and the use of inefficient nonlinear crystals, thereby simplifying the experimental procedure. Moreover, the LDQS scheme provides a greater enhancement in entanglement when both schemes are implemented with the same success probability. Finally, we also demonstrate that the LDQS operation can be used to enhance the entanglement of the TMSV state in lossy channels. These advantages suggest that our scheme shows promise for application in various quantum information tasks, including quantum metrology and quantum communication. • Enhancing entanglement with local displacement-based quantum scissor scheme. • The scheme is easier to implement than the local squeezing-based quantum scissor. • The scheme exhibits robustness against entanglement degradation.

The entanglement improvement is theoretically investigated when applying a single-side quantum scissors (SSQS) with a local squeezing operation and two-asymmetrical beam splitters (BSs) to one mode of an input two-mode squeezed vacuum state (TMSV). It is found that the gain factor can be significantly enhanced with the increasing of local squeezing parameter at the expense of the success probability. The entanglement can also be further improved adjusting the local-squeezing or the transmissivity of BSs in a small initial squeezing region. In addition, our scheme is robust against the photon loss in TMSV. The improved effect becomes more obvious due to the presence of local squeezing. However, the case is not true for a more realistic SSQS. In both cases, the asymmetric BSs play a positive role for the entanglement improvement. These results suggest that the squeezing-based SSQS at single-photon level is beneficial to effectively improve the entanglement, which may have potential applications in quantum communication.

In quantum information processing, the preparation and optimization of entanglement sources are critical steps. This paper explores reality-enhanced entanglement in two-mode squeezed vacuum states via three-photon quantum scissors (3-QS). Crucially, in realistic scenarios, the optimized 3-QS scheme achieves stronger entanglement than ideal scenarios while expanding the effective enhancement range. By adjusting beam-splitter transmittance in experimentally accessible weak squeezing regimes, we achieve enhanced entanglement and higher quantum teleportation fidelity compared to conventional strong squeezing approaches. This scheme provides a practical path toward long-distance quantum communication by transforming low-quality squeezed states into high-fidelity entanglement resources.

We propose a theoretical scheme for entanglement distillation of the two-mode squeezed vacuum state (TMSVS) by nondeterministic optical nonlinear amplification based on the work of Anisimov et al. [Phys. Rev. Lett.104, 103602 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.103602]. By applying the quantum-scissors operations to both modes of the TMSVS, only the twin vacuum and the twin one-photon components can survive in the resulting state. We show that both entanglement and squeezing can be enhanced in the high-transmissivity and low-squeezing region. In addition, a comparison with symmetrical single-photon subtraction and quantum catalysis shows that the proposed states can achieve a better entanglement enhancement than the photon subtraction in a high-transmissivity region, and a similar property is shared by the catalyzed states in low-transmissivity regions.

We present a strong quantum entanglement generation protocol based on two-mode photon-subtracted squeezed vacuum (TMPSSV) states. The generated entanglement shows higher entropy than those based on quantum catalysis, quantum scissors, photon-subtracted two-mode squeezed vacuum (PSTMSV) states, nonlocal PSTMSV states, and two-mode squeezed vacuum (TMSV) states in the ideal case. The impacts of experimental imperfections such as losses in the squeezed vacuum states and detection efficiency of single-photon detectors on the generated entanglement based on TMPSSV states are analyzed. When practical experimental imperfections are considered, higher logarithmic negativity than those of ideal PSTMSV states and ideal TMSV states are obtained for low initial squeezing level. Enhancement factor over 2 is obtained when the entanglement generated from imperfect non-Gaussian states passes through two lossy quantum channels in low initial squeezing level. Strong correlation is kept in lossy channels, which shows good robustness of the entanglement generation protocol based on TMPSSV states.

We study entanglement concentration of continuous-variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum (i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter), which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one or on both of the modes and show that local displacements can lead to improved performance of the concentration protocol.

From the perspective of majorization theory, we study how to enhance the entanglement of a two-mode squeezed vacuum (TMSV) state by using local filtration operations. We present several schemes achieving entanglement enhancement with photon addition and subtraction, and then consider filtration as a general probabilistic procedure consisting in acting with local (nonunitary) operators on each mode. From this, we identify a sufficient set of two conditions for these filtration operators to successfully enhance the entanglement of a TMSV state, namely, the operators must be Fock orthogonal (i.e., preserving the orthogonality of Fock states) and Fock amplifying (i.e., giving larger amplitudes to larger Fock states). Our results notably prove that ideal photon addition, subtraction, and any concatenation thereof always enhance the entanglement of a TMSV state in the sense of majorization theory. We further investigate the case of realistic photon addition (subtraction) and are able to upper bound the distance between a realistic photon-added (-subtracted) TMSV state and a nearby state that is provably more entangled than the TMSV, thus extending entanglement enhancement to practical schemes via the use of a notion of approximate majorization. Finally, we consider the state resulting from

k

-photon addition (on each of the two modes) on a TMSV state. We prove analytically that the state corresponding to

k=1

majorizes any state corresponding to $2\ensuremath{\le}k\ensuremath{\le}8$ and we conjecture the validity of the statement for all $k\ensuremath{\ge}9$.