Genuine Entanglement detection via Projection map in multipartite system
- URL: http://arxiv.org/abs/2401.03052v1
- Date: Fri, 5 Jan 2024 20:06:42 GMT
- Title: Genuine Entanglement detection via Projection map in multipartite system
- Authors: Bivas Mallick, Sumit Nandi
- Abstract summary: We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map.
We have shown that projection map can detect both inequivalent SLOCC classes of genuine entanglement in tripartite scenario.
We also construct a general framework to certify genuine multipartite entanglement for arbitrary N-qubit states.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present a formalism to detect genuine multipartite entanglement by
considering projection map which is a positive but not completely positive map.
Projection map has been motivated from no-pancake theorem which repudiates the
existence of a quantum operation that maps the Bloch sphere onto a disk along
its equator. The not-complete positivity feature of projection map is explored
to investigate its credibility for certifying bi-separability in multipartite
quantum systems. We have lifted projection map to derive a separability
criterion in order to ascertain bi-separability in tripartite scenario. We have
shown that projection map can detect both inequivalent SLOCC classes of genuine
entanglement in tripartite scenario i.e. W state and GHZ state. Also, we have
shown that projection map is robust against white noise. We also construct a
general framework to certify genuine multipartite entanglement for arbitrary
N-qubit states by lifting projection map. The efficacy of our framework is
further explored to detect quadripartite GHZ state.
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