Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories

TL;DR

This paper explores the complex entanglement structures in general probabilistic theories, revealing that self-duality and local unitary symmetry do not uniquely determine standard entanglement configurations, and introduces conditions for entanglement detection.

Contribution

It demonstrates the existence of multiple self-dual, locally symmetric entanglement structures and provides a finite minimization method for entanglement detection.

Findings

Existence of infinite self-dual, locally symmetric entanglement structures

Non-orthogonal states can be perfectly distinguishable in certain structures

Finite parameterized minimizations can detect entanglement

Abstract

We study the entanglement structure, i.e., the structure of quantum composite system from operational aspects. The structure is not uniquely determined in General Probabilistic Theories (GPTs) even if we impose reasonable postulate about local systems. In this paper, we investigate the possibility that the standard entanglement structure can be determined uniquely by repeatability of measurement processing and its saturated situation called self-duality. Surprisingly, self-duality cannot determine the standard entanglement structure even if we additionally impose local unitary symmetry assumption. In this paper, we show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. Besides, we also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable. In addition, as a byproduct, we derive an sufficient condition to achieve the detection of the entanglement property with a finite number of parameterized minimizations.