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arXiv:2206.01800 · Physical Review A

Optimal entanglement enhancing via conditional measurements

Jiru Liu, Yusef Maleki, Muhammad Suhail Zubairy

Published Jun 3, 2022• 8 citations
arXivHTMLPDF

Abstract

Enhancing quantum entanglement is important for many quantum information processing applications. In this paper, we consider a protocol for entanglement enhancing in a two-mode squeezed vacuum state (TMSVS), attained based on photon subtraction, photon catalysis, and photon addition. Central to such an operation is the task of mixing and detecting number states with each mode of TMSVS. We analyze various settings and find an optimal setup for improving the entanglement of the state.

DOI
10.1103/physreva.105.062405

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Enhancing quantum entanglement is important for many quantum information processing applications. In this paper, we consider a protocol for entanglement enhancing in a two-mode squeezed vacuum state (TMSVS), attained based on photon subtraction, photon catalysis, and photon addition. Central to such an operation is the task of mixing and detecting number states with each mode of TMSVS. We analyze various settings and find an optimal setup for improving the entanglement of the state.
I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantum teleportation) in certain parameter ranges spanned by the low transmissivities of the BSs and the small squeezing parameter of the input TMSVS.
We investigate the entanglement enhancement of the two-mode squeezed vacuum state using various combinations of photon additions and photon subtractions. We suppose that a sequence of N operations are performed on each mode and on a single mode of the two-mode squeezed vacuum state, each operation being photon addition or photon subtraction; then there are 2N possible combinations of operations in total. We calculate the entanglement for all the photon-added/subtracted states generated by all possible combinations for N=2, N=3, and N=4, respectively, and deduce that the combination of operations alternating between photon addition and photon subtraction enhances the entanglement most effectively, while adding or subtracting N photons repeatedly enhances the entanglement least effectively.
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.
Abstract Multiphoton catalysis is a non-Gaussian operation which has aroused interest recently in quantum information processing. There are two schemes of multiphoton catalysis in the current literature: one uses a beam splitter, while the other uses an optical parametric amplifier. We derive the catalysis operator in the Fock basis for each scheme and find a close relationship between them. We propose to enhance quantum entanglement of the two-mode squeezed vacuum state by performing two-mode multiphoton catalysis independently using two beam splitters. We calculate the optimal entanglement, which is maximized over two independent transmissivities, for the catalyzed states with various pairs of catalysis photon numbers, and find that in each case entanglement is enhanced only when the squeezing parameter is below a certain threshold. We also find that the optimal entanglement is nonzero in the limit of low squeezing, and deduce the analytical forms of the limiting catalyzed state and its entanglement in each case from numerical coefficients.
We investigate the problem of enhancing quantum entanglement of the two-mode squeezed vacuum state by asymmetric combinations of photon additions and subtractions. Suppose a combination of N operations is performed on the two-mode squeezed vacuum state, in which each operation may be either photon addition or photon subtraction and may be performed on either mode A or mode B of the state; then there are (N+1)2N possible combinations in all. We calculate in detail the entanglement enhancement by all possible combinations for each given N∈{1,2,…,5,6}, respectively, and find that when the squeezing parameter is small, combinations such as aa†aa†…, a†aa†a…, and their equivalent ones always achieve the greatest enhancement of entanglement, while combinations such as aaaa…, a†a†a†a†…, and their equivalent ones always achieve the lowest enhancement of entanglement; when the squeezing parameter is great enough, entanglement enhancement by each combination is nearly the same. We also compare the maximal and minimal entanglement achieved by such combinations for N=1 to 6, and find that when the squeezing parameter is small, a combination of more operations may generate even less entanglement than a combination of fewer operations.