相关论文: Cauchy-Schwarz inequality and particle entanglemen…

Basing on the analogy between the coherent states of light and separable states of $N$ bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent…

Destructive interference-based photon-phonon antibunching can lead to violations of classical inequalities in optomechanical cavity systems. In this paper, we explore the violation of the classical Cauchy-Schwarz inequality by examining…

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…

Quantum optics bridges esoteric notions of entanglement and superposition with practical applications like metrology and communication. Throughout, there is an interplay between information theoretic concepts such as entropy and physical…

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 It\^o equations derived from the positive-P representation of the…

The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidences of the genuinely quantum nature of an emitter. We show that by dispensing from the usual approximation of mode correlations and studying directly…

A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which…

Motivated by some applications to calculating order of poles of certain (local or global) $L$-functions, the author considers a Cauchy-Schwarz type inequality for representations of SU(2).

Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…

Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well…

This thesis investigates quantum cloning and related quantum entanglement problems using core concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its…

We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added…

Particle identity and entanglement are two fundamental quantum properties that work as major resources for various quantum information tasks. However, it is still a challenging problem to understand the correlation of the two properties in…

We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain…

Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…

The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Due to their exchange symmetry, identical particles can appear to be entangled -- another uniquely quantum…

Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…

We discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakovsky inequalities. In this note some rigorous…

It was shown recently that entanglement of identical particles has a feature called dualism [Phys. Rev. Lett. 110, 140404 (2013)], which is fundamentally connected with quantum indistinguishability. Here we report an experiment that…

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability…