Separability of Bosonic Systems

Abstract

In this paper, we study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive Matrices" is drawn. Such connection is employed to demonstrate that multi-qubit quantum states with Dicke states being its eigenvectors is separable if and only if two related Hankel matrices are positive semidefinite. By employing this criterion, we are able to show that such state is separable if and only if it's partial transpose is non-negative, which confirms the conjecture in [Wolfe, Yelin, Phys. Rev. Lett. (2014)]. Then, we present a class of bosonic states in $d\otimes d$ system such that for general $d$, determine its separability is NP-hard although verifiable conditions for separability is easily derived in case $d=3,4$.

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• Imbalance Entanglement: Symmetry Decomposition of Negativity
• Classical simulation of photonic linear optics with lost particles
• Separability of diagonal symmetric states: a quadratic conic optimization problem
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• Genuine Multipartite Correlations in a Boundary Time Crystal
• Non-classical correlations in quantum mechanics and beyond
• Entanglement and Nonlocality in Diagonal Symmetric States of $N$-qubits
• Detecting mixed-unitary quantum channels is NP-hard
• Separability of Completely Symmetric States in Multipartite System
• Entanglement properties of quantum grid states
• Entangled symmetric states and copositive matrices
• Dephasing-assisted entanglement in a system of strongly coupled qubits
• Spectral Properties of Symmetric Quantum States and Symmetric Entanglement Witnesses
• Certificates of quantum many-body properties assisted by machine learning
• Unraveling Dicke Superradiant Decay with Separable Coherent Spin States
• Can entanglement hide behind triangle-free graphs?
• Genuine multipartite correlations in Dicke Superradiance
• Multipartite entanglement in the diagonal symmetric subspace
• Introduction to quantum entanglement in many-body systems
• Necessary and sufficient condition of separability for D-symmetric diagonal states
• Symmetric quantum states: a review of recent progress
• Random covariant quantum channels
• Revealing hidden physical nonclassicality with nonnegative polynomials
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Absence of Entanglement Growth in Dicke Superradiance
• Dicke subsystems are entangled
• Entanglement in the Dicke subspace
• Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)