Violation of the Cauchy-Schwarz Inequality in the Macroscopic Regime

Cauchy-Schwarz characterization of tripartite quantum correlations in an optical parametric oscillator

We analyze the three-mode correlation properties of the electromagnetic field in a optical parametric oscillator below threshold. We employ a perturbative expansion of the Itô equations derived from the positive-P representation of the density matrix. Using the generalized Cauchy-Schwarz inequality, we investigate the genuine quantum nature of the triple correlations between the interacting fields, since in this case continuous variable entanglement is not detected by the van Loock-Furusawa criterion [Phys. Rev. A {\bf 67}, 052315 (2003)]. Although not being a necessary condition, these triple…

基于柯西-施瓦茨不等式的混合态纠缠

Mixed State Entanglement Via the Cauchy-Schwarz Inequality

针对常用混合态纠缠度量难应用、难关联系统物理性质的问题，提出依赖密度算符布居与相干的CSV纠缠充分条件，可直接关联系统对称性等特征，并在三类模型中验证其能提供新洞见。

Improving the Cauchy-Schwarz inequality

We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy-Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in certain singular situations where the celebrated inequality appears to be useless. The basic tenet generates a few other interesting relations, including the improvements over certain common uncertainty bounds. Role of projection operators in modifying the Cauchy-Schwarz relation is noted. Selected applications reveal the efficacy.

Cauchy-Schwarz inequality and particle entanglement

The Glauber-Sudarshan $P$-representation is used in quantum optics to distinguish between semi-classical and genuinely quantum electromagnetic fields. We employ the analog of the $P$-representation to show that the violation of the Cauchy-Schwarz inequality for the second-order correlation function is a proof of entanglement between identical massive bosons. The presented derivation is valid both in systems with fixed and fluctuating number of particles. Thanks to the recent advances in techniques of detecting positions of separate particles, the violation of the Cauchy-Schwarz inequality can …

混合电磁子系统中鲁棒非经典磁振子对的产生与柯西-施瓦茨不等式违反

Robust Nonclassical magnon pair generation and Cauchy-Schwarz inequality violation in a hybrid electromagnonic system

该研究在混合电磁子系统中，利用驱动相位补偿耦合不对称性，实现鲁棒非经典磁振子对产生与柯西-施瓦茨不等式违反，为相位可控的磁振子量子信息处理提供支持。

非相对论量子电动力学中截断模型精度的Cauchy-Schwarz界

Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics

本文利用Cauchy-Schwarz不等式给出截断光-物质理论精度的普遍界限，并证明截断空间内的幺正旋转不能实现规范变换，指出文献中广泛使用的Coulomb规范模型存在错误预测。

Violation of the Cauchy-Schwarz inequality with matter waves

The Cauchy-Schwarz (CS) inequality -- one of the most widely used and important inequalities in mathematics -- can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum mechanical correlations can, however, exceed classical bounds.Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The correlated atoms have large spatial separations and therefore open new oppo…

耦合光机械系统中的柯西-施瓦茨与贝尔不等式违背

Cauchy-Schwarz and Bell Inequality Violations in Coupled Optomechanical Systems

本文研究双弱探测场驱动的耦合光机械系统中光子-声子反聚束导致的柯西-施瓦茨不等式与贝尔不等式违背，揭示强量子关联及反对角滤波模式，为按需产生单光子-声子对提供依据。

Violation of Cauchy-Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic h…

推广柯西-施瓦茨不等式：Hadamard幂与张量积

Generalizing the Cauchy-Schwarz inequality: Hadamard powers and tensor products

该研究推广了一类柯西-施瓦茨型不等式，给出三种新阐释性证明，并从向量到矩阵、非2指数、多向量三个方向拓展了该不等式的适用范围。

Generalized distillability conjecture and generalizations of Cauchy-Bunyakovsky-Schwarz inequality and Lagrange identity

Let rho_k, k=1,2,...,m, be the critical Werner state in a bipartite d_k by d_k quantum system, i.e., the one that separates the 1-distillable Werner states from those that are 1-indistillable. We propose a new conjecture (GDC) asserting that the tensor product of rho_k is 1-indistillable. This is much stronger than the familiar conjecture saying that a single critical Werner state is indistillable. We prove that GDC is true for arbitrary m provided that d_k is bigger than 2 for at most one index k. We reformulate GDC as an intriguing inequality for four arbitrary complex hypermatrices of type …

A general inseparability criterion for non-Gaussian states

We have derived a general separability criterion for a class of two mode non-Gaussian continuous variable systems, obtained earlier using PPT, violation of which provides sufficient condition for entanglement. It has been obtained by utilizing the Cauchy-Schwarz inequality and from the basic definition of separable states. This criterion coincides with the work of Agarwal and Biswas [4] which involved inequality involving higher order correlation, for testing entanglement in non-Gaussian states.