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

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.

13 pages, will appear in Journal of Physics A: Mathematical and Theoretical

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Faster than Hermitian Quantum Mechanics
• Increase of entanglement by local PT -symmetric operations

Cited by in corpus (7)

• Interpretation of quantum mechanics with indefinite norm
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Unconventional steady states and topological phases in an open two-level non-Hermitian system
• Local preservation of no-signaling in multiparty PT-symmetric evolutions
• Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics
• Extracting the internal nonlocality from the dilated Hermiticity
• Necessary condition for information transfer under simulated parity-time-symmetric evolution