Entanglement-fluctuation relation for bipartite pure states

Abstract

We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N-level subsystem. We express this polarization fluctuation in terms of subsystem purity and other entanglement measures. The derived fluctuation-entanglement relation is evaluated for the ground states of a one-dimensional free fermion gas and the Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for experimentally measuring entanglement using Stern-Gerlach-type state selectors.Comment: 7 pages, 1 figure. Revisions, corrections, title change made. References updated. New example adde

Integer effects in the entanglement and spin fluctuations of a quantum Hall system with Rashba interactions

“…We report clear signatures in the average transverse polarization of crossings between the highest occupied energy level and the lowest unoccupied level at special values of the filling factor. Furthermore, since subsystem fluctuations in bipartitioned systems are indicators of entanglement [36][37][38] we demonstrate that the integer eects observed in the SOEE are also manifested in the polarization fluctuations.…”

“…As seen in figure 3 An exact quantitative relationship between these fluctuations and the spin-orbit entanglement can be made by applying an entanglement-fluctuation relation [38] for each occupied single-electron state. It turns out that the transverse polarization fluctuation for an electron in the state σ m, is directly related to entanglement measures such as the purity…”

Entanglement entropy of the maximum geminal of the BCS ground state

“…In a topologically ordered system, the EE also diverges logarithmically [7][8][9][10]. Additionally, in various fermion systems, logarithmical behaviors of the EE have been observed [11][12][13][14][15][16][17][18]. Further in systems with long-range order, such as ferromagnetism [19], anti-ferromagnetism [19], and Bose-Einstein condensation (BEC) [20][21][22][23][24], the logarithmical contributions to the EE have been confirmed.…”

Quantum fluctuation of entanglement for accelerated two-level detectors*

“…Thus, the calculation of the entanglement fluctuation will reduce to the determination of the concurrence. Now the fluctuation of quantum entanglement with the arbitrary bipartite system is quantified as [40,41]…”