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Allowing the iteration points to move outside of S may result in large absolute values of the angles, possibly leading to reduced precision in the output. Such effects can be prevented by projecting the current iteration point back to S a few times in the first couple of iterations.
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The entanglement of ρ (η) (and other states) has also been studied in Ref. in terms of the "global robustness". The search over all separable (pure and mixed) states appearing in the evaluation of this measure could in principle also be accomplished with the parametrized quasi-Newton method (similar in spirit to Sec. 3).
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The subsystem linear entropy SL (|ψ) =2 [1-Tr (ρ 2)], where ρ = TrB |ψ ψ|, is a well-established bipartite entanglement measure that is often used instead of the von Neumann entropy in order to simplify calculations.
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The subsystem linear entropy SL (|ψ) =2 [1-Tr (ρ 2)], where ρ = TrB |ψ ψ|, is a well-established bipartite entanglement measure that is often used instead of the von Neumann entropy in order to simplify calculations.
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We mention, however, that there are also measures of entanglement which are not maximized by the n -partite GHZ state Eq. 1. Moreover, some measures ascribe this state an unexpectedly low amount of entanglement for n>3. See, e.g., Ref. for an extensive numerical study.
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We mention, however, that there are also measures of entanglement which are not maximized by the n -partite GHZ state Eq. 1. Moreover, some measures ascribe this state an unexpectedly low amount of entanglement for n>3. See, e.g., Ref. for an extensive numerical study.
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Since for the number of particles N considered in Sec. 4 the splitting between the lowest and the next-higher multiplets is still always large compared to temperature, we diagonalize only the lowest-lying (N+1) -dimensional subspace of H using a Lanczos algorithm
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Since for the number of particles N considered in Sec. 4 the splitting between the lowest and the next-higher multiplets is still always large compared to temperature, we diagonalize only the lowest-lying (N+1) -dimensional subspace of H using a Lanczos algorithm.
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