# Consistency of PT-symmetric quantum mechanics

@article{Brody2016ConsistencyOP, title={Consistency of PT-symmetric quantum mechanics}, author={Dorje C. Brody}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2016}, volume={49} }

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…

## 53 Citations

### Observation of PT-symmetric quantum interference

- PhysicsNature Photonics
- 2019

Parity-Time (PT) symmetric quantum mechanics is a complex extension of conventional Hermitian quantum mechanics in which physical observables possess a real eigenvalue spectrum. However, an…

### PT-symmetry, indefinite metric, and nonlinear quantum mechanics

- Physics
- 2017

If a Hamiltonian of a quantum system is symmetric under space-time reflection, then the associated eigenvalues can be real. A conjugation operation for quantum states can then be defined in terms of…

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- Physics
- 2019

Recently, apparent non-physical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the non-signaling theorem,…

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- PhysicsPhysical Review A
- 2019

Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem,…

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- PhysicsPhysical Review A
- 2019

The time-dependent pseudo-Hermitian formulation of quantum mechanics allows to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of…

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- PhysicsScientific reports
- 2016

It is shown that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum, and expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium.

### Comparing Hermitian and Non-Hermitian Quantum Electrodynamics

- PhysicsSymmetry
- 2022

In recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries.…

### PT symmetry and the evolution speed in open quantum systems 1

- PhysicsJournal of Physics: Conference Series
- 2021

The dynamics of an open quantum system with balanced gain and loss is not described by a PT-symmetric Hamiltonian but rather by Lindblad operators. Nevertheless the phenomenon of PT-symmetry breaking…

### Fe b 20 16 Non-hermitian quantum thermodynamics

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- 2018

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum…

### O ct 2 01 6 Pseudo-Hermitian systems with PT-symmetry : Degeneracy and Krein space

- Physics, Mathematics
- 2016

We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT -symmetry (P = 1,T 2 = 1) admit a degeneracy structure. This kind of degeneracy is expected traditionally in the…

## References

SHOWING 1-10 OF 56 REFERENCES

### Observation of parity–time symmetry in optics

- Physics
- 2010

One of the fundamental axioms of quantum mechanics is associated with the Hermiticity of physical observables 1 . In the case of the Hamiltonian operator, this requirement not only implies real…

### PT -symmetric Hamiltonians and their application in quantum information

- Physics, Computer Science
- 2015

It is concluded that such evolution is unlikely to provide any benefit over existing techniques, and three inequivalent experimental implementations of PT -symmetric Hamiltonians are proposed, with careful attention to the resources required for each such evolution.

### Quasi-Hermitian operators in quantum mechanics and the variational principle

- Mathematics, Physics
- 1992

### Exact PT-symmetry is equivalent to Hermiticity

- Physics, Mathematics
- 2003

We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator…

### Biorthogonal quantum mechanics

- Physics
- 2013

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose…

### symmetry as a generalization of Hermiticity

- Physics
- 2010

The Hilbert space in -symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general -symmetric matrix Hamiltonians are constructed for the 2 × 2…

### Faster than Hermitian quantum mechanics.

- PhysicsPhysical review letters
- 2007

The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole and may have applications in quantum computing.

### Stationary states of a PT symmetric two-mode Bose–Einstein condensate

- Physics
- 2012

The understanding of nonlinear PT symmetric quantum systems, arising for example in the theory of Bose–Einstein condensates in PT symmetric potentials, is widely based on numerical investigations,…

### Biorthogonal quantum systems

- Physics
- 2007

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially…

### PT symmetry and spontaneous symmetry breaking in a microwave billiard.

- PhysicsPhysical review letters
- 2012

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the…