Most symmetric separable states with conserved charge N are not symmetrically separable, with number entanglement showing Gaussian concentration around a strictly positive value.
On the volume of the set of mixed entangled states
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abstract
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, while separability is connected with quantum mixtures. In particular, states of sufficiently low purity are necessarily separable.
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UNVERDICTED 4representative citing papers
Lower bounds on the best separable approximation distance for non-pure spin-squeezed states are obtained from the complete set of spin-squeezing inequalities, with symmetry-exploiting optimization for upper bounds, revealing finite-temperature entanglement in ordered phases of the XXZ model.
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane bulk geometries.
citing papers explorer
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The typicality of symmetry-induced entanglement
Most symmetric separable states with conserved charge N are not symmetrically separable, with number entanglement showing Gaussian concentration around a strictly positive value.
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Estimating the best separable approximation of non-pure spin-squeezed states
Lower bounds on the best separable approximation distance for non-pure spin-squeezed states are obtained from the complete set of spin-squeezing inequalities, with symmetry-exploiting optimization for upper bounds, revealing finite-temperature entanglement in ordered phases of the XXZ model.
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Separability and entanglement of resonating valence-bond states
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
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Holographic entanglement entropy and complexity for the cosmological braneworld model
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane bulk geometries.