近日，美国亚利桑那大学的Zacharie Van Herstraeten与比利时布鲁塞尔自由大学的Nicolas J. Cerf等人合作并取得一项新进展。经过不懈努力，他们提出局部滤波增强纠缠的优化理论方法。相关研究成果已于2024年10月28日在国际知名学术期刊《物理评论A》上发表。

从控制不等式理论的角度出发，该研究团队研究了如何通过局部滤波操作来增强双模压缩真空（TMSV）态的纠缠。研究人员提出了几种通过光子加减实现纠缠增强的方案，然后将滤波视为一种通用的概率过程，即对每个模式施加局部（非幺正）算符。

基于此，研究人员确定了这些滤波算符成功增强TMSV态纠缠的两个充分条件：算符必须是福克正交的（即保持福克态的正交性）和福克放大的（即给予更大的福克态更大的振幅）。这项研究结果显著证明，从控制不等式理论的角度来看，理想的光子加法、减法以及它们的任意组合总是能够增强TMSV态的纠缠。

研究人员还进一步研究了实际光子加法（减法）的情况，并能够限制实际加（减）光子TMSV态与附近一个已证明比TMSV态更纠缠的态之间的距离，从而通过近似控制不等式的概念将纠缠增强扩展到实际方案中。

最后，研究人员考虑了TMSV态经k光子加法（在每个模式上）后得到的状态。他们通过分析证明，k=1对应的状态控制不等式化任何2≤k≤8对应的状态，并推测该结论对所有k≥9都成立。

附：英文原文

Title: Majorization theoretical approach to entanglement enhancement via local filtration

Author: Zacharie Van Herstraeten, Nicolas J. Cerf, Saikat Guha, Christos N. Gagatsos

Issue&Volume: 2024/10/28

Abstract: 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≤k≤8 and we conjecture the validity of the statement for all k≥9.

DOI: 10.1103/PhysRevA.110.042430

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.042430