# No-signaling principle and Bell inequality in PT-symmetric quantum mechanics

## TL;DR

This paper demonstrates that PT-symmetric quantum mechanics, despite previous challenges, can uphold the no-signaling principle, preserve entanglement, and satisfy Bell inequalities, thus supporting its consistency as a fundamental quantum theory.

## Contribution

The study revisits the no-signaling principle within PT-symmetric quantum mechanics and shows it remains valid, ensuring the theory's consistency with fundamental quantum principles.

## Key findings

- No-signaling principle is preserved in PT-symmetric two-qubit systems.
- Entanglement invariance is reaffirmed under PT-symmetric framework.
- CHSH inequality is satisfied in the PT-symmetric quantum mechanics context.

## Abstract

PT-symmetric quantum mechanics, the extension of conventional quantum mechanics to the non-Hermitian Hamiltonian invariant under the combined parity (P) and time reversal (T) symmetry, has been successfully applied to a variety of fields such as solid state physics, mathematical physics, optics, quantum field theory. Recently, the extension of PT-symmetrical theory to entangled quantum systems was challenged in that PT formulation within the conventional Hilbert space violates the no-signaling principle. Here, we revisit the derivation of non-signaling principle in the framework of PT inner product prescription. Our results preserve the no-signaling principle for a two-qubit system, reaffirm the invariance of the entanglement, and reproduce the Clauser-Horne-Shimony-Holt (CHSH) inequality. We conclude that PT-symmetric quantum mechanics satisfies the requirements for a fundamental theory and provides a consistent description of quantum systems.