Enhanced entanglement criterion via symmetric informationally complete measurements

Abstract

We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection.

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

“…This amounts to bounding the value of A achievable under any twoor three-outcome qubit POVM and then observing a violation of that bound. For this purpose, one may employ the hierarchy of dimensionally bounded quantum correlations [38] which can be used to upper bound A under three-outcome POVMs 3 . To obtain tight bounds, one may need a reasonably high hi-erarchy level which can be efficiently implemented using the methods of Ref.…”

“…The effort needed to evaluate the bound depends on the chosen prepareand-measure scenario. Typically, considering scenarios with some symmetry properties is beneficial 3. The hierarchy is built on projective measurements.…”

Entanglement criterion via general symmetric informationally complete measurements

“…Entanglement detection via SIC-POVMs had been discussed in [38]. However, the method subjects to the existence of SIC-POVMs, which is an open problem.…”

“…Remark 1. If one takes a = 1 d 2 , the criterion of Theorem 1 reduces to the criterion based on SIC-POVM [38], i.e., if a bipartite state ρ is separable, then P tr…”

“…In addition, the authors in [37] considered a nonlinear entanglement criterion based on SIC-POVMs. In Shang et al [38], the authors used the SIC-POVMs to derive the entanglement criterion and demonstrated the superiority of the criterion by various examples.…”