Separability gap and large deviation entanglement criterion

Abstract

For a given Hamiltonian $H$ on a multipartite quantum system, one is interested in finding the energy $E_0$ of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one looks for the minimal expectation value ${\lambda }_{\min }^{\otimes }$ of $H$ among all product states. For several concrete model Hamiltonians, we investigate the difference ${\lambda }_{\min }^{\otimes }-E_0$, called separability gap, which vanishes if the ground state has a product structure. In the generic case of a random Hermitian matrix of the Gaussian orthogonal ensemble, we find explicit bounds for the size of the gap which depend on the number of subsystems and hold with probability one. This implies an effective entanglement criterion applicable for any multipartite quantum system: If an expectation value of a typical observable among a given state is sufficiently distant from the average value, the state is almost surely entangled.

arXiv comment8 pages total, 3 figures

References in corpus (29)

• Quantum entanglement
• Quantum Computing in the NISQ era and beyond
• Decoherence, einselection, and the quantum origins of the classical
• Area laws for the entanglement entropy - a review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum annealing with more than one hundred qubits
• Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
• Global entanglement in multiparticle systems
• Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer
• Induced measures in the space of mixed quantum states
• Aspects of generic entanglement
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Introduction to Random Matrices - Theory and Practice
• Entanglement in a quantum annealing processor
• Magnetic Susceptibility as a Macrosopic Entaglement Witness
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• Demonstration of nonstoquastic Hamiltonian in coupled superconducting flux qubits
• Generic local distinguishability and completely entangled subspaces
• Topology trivialization and large deviations for the minimum in the simplest random optimization
• Classical Particle in a Box with Random Potential: exploiting rotational symmetry of replicated Hamiltonian
• Restricted numerical range: a versatile tool in the theory of quantum information
• Quantum fluctuation theorem to benchmark quantum annealers
• Disorder-Induced Order in Quantum XY Chains
• Quantum neural networks to simulate many-body quantum systems
• Product numerical range in a space with tensor product structure
• Positive maps, positive polynomials and entanglement witnesses
• On the phase diagram of the anisotropic XY chain in transverse magnetic field

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