Fraction of isospectral states exhibiting quantum correlations

Abstract

For several types of correlations: mixed-state entanglement in systems of distinguishable particles, particle entanglement in systems of indistinguishable bosons and fermions and non-Gaussian correlations in fermionic systems we estimate the fraction of non-correlated states among the density matrices with the same spectra. We prove that for the purity exceeding some critical value (depending on the considered problem) fraction of non-correlated states tends to zero exponentially fast with the dimension of the relevant Hilbert space. As a consequence a state randomly chosen from the set of density matrices possessing the same spectra is asymptotically a correlated one. To prove this we developed a systematic framework for detection of correlations via nonlinear witnesses.

7 pages, 1 figure, title changed, abstract and introduction rewritten, one reference added

References in corpus (1)

• Extracting entanglement from identical particles

Cited by in corpus (17)

• Entanglement in indistinguishable particle systems
• Random matrix techniques in quantum information theory
• Random bosonic states for robust quantum metrology
• Classical simulation of photonic linear optics with lost particles
• Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states
• Bipartite entanglement in fermion systems
• Classical simulation of fermionic linear optics augmented with noisy ancillas
• Quantum Operations in an Information Theory for Fermions
• Fermionic Entanglement in Superconducting Systems
• One-body entanglement as a quantum resource in fermionic systems
• One-body information loss in fermion systems
• Quantum marginals from pure doubly excited states
• Beating detection loophole in nonlinear entanglement witnesses
• Random matrices with prescribed eigenvalues and expectation values for random quantum states
• Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state
• Measurement-device-independent nonlinear entanglement witnesses
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses