Consistency of PT-symmetric quantum mechanics

Abstract

In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric---the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.

6 pages, final version to appear in J Phys A

References in corpus (14)

• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Faster than Hermitian Quantum Mechanics
• Mixed-state evolution in the presence of gain and loss
• Bypassing the bandwidth theorem with PT symmetry
• Increase of entanglement by local PT -symmetric operations
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• PT spectroscopy of the Rabi problem
• The role of the geometric phases in adiabatic populations tracking for non-hermitian hamiltonians
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models
• Random matrix ensembles for $PT$-symmetric systems
• Supersymmetric Biorthogonal Quantum Systems

Cited by in corpus (46)

• Symmetry and Topology in Non-Hermitian Physics
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Parity-time-symmetric topological superconductor
• Observation of PT-symmetric quantum interference
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Hamiltonian for the zeros of the Riemann zeta function
• Non-hermitian quantum thermodynamics
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
• Maxwell meets Reeh-Schlieder: the quantum mechanics of neutral bosons
• Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Hidden PT Symmetry and quantization of coupled-oscillators model of QASER
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Parameter estimation and quantum entanglement in PT symmetrical cavity magnonics system
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Holonomic Gates in Pseudo-Hermitian Quantum Systems
• Quantum deleting and cloning in a pseudo-unitary system
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• Observing a Changing Hilbert-Space Inner Product
• Spectrum and normal modes of non-hermitian quadratic boson operators
• Proposal of a quantum version of active particles via a nonunitary quantum walk
• Modal Purcell factor in $\mathcal{P}\mathcal{T}$-symmetric waveguides
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Comparing Hermitian and Non-Hermitian Quantum Electrodynamics
• Multitude of exceptional points in van der Waals magnets
• Topological invariants of complex energy plane in non-Hermitian systems
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
• Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss
• Local preservation of no-signaling in multiparty PT-symmetric evolutions
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial $\mathcal{P}\mathcal{T}$-symmetry and Higgs algebra
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• A non-trivial PT-symmetric continuum Hamiltonian and its Eigenstates and Eigenvalues
• Decomposition of a system in pseudo-Hermitian quantum mechanics
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Stronger sum uncertainty relations for non-Hermitian operators
• Geometric criterion of topological phase transition for non-Hermitian systems
• On the $\mathcal{P}\mathcal{T}$-symmetric parametric amplifier
• Reduced dynamics in quasi-Hermitian systems
• PT symmetry and the evolution speed in open quantum systems