Observing a changing Hilbert-space inner product

@article{Karuvade2022ObservingAC,
  title={Observing a changing Hilbert-space inner product},
  author={Salini Karuvade and Abhijeet Alase and Barry C. Sanders},
  journal={Physical Review Research},
  year={2022}
}
In quantum mechanics, physical states are represented by rays in Hilbert space H , which is a vector space imbued by an inner product 〈 | 〉, whose physical meaning arises as the overlap 〈φ|ψ〉 for |ψ〉 a pure state (description of preparation) and 〈φ| a projective measurement. However, current quantum theory does not formally address the consequences of a changing inner product during the interval between preparation and measurement. We establish a theoretical framework for such a changing inner… 

Figures from this paper

References

SHOWING 1-10 OF 75 REFERENCES

Energy observable for a quantum system with a dynamical Hilbert space and a global geometric extension of quantum theory

A non-Hermitian operator may serve as the Hamiltonian for a unitary quantum system, if we can modify the Hilbert space of state vectors of the system so that it turns into a Hermitian operator. If

Quantum Brachistochrone problem and the geometry of the state space in pseudo-Hermitian quantum mechanics.

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for

PT-symmetric quantum state discrimination

TLDR
The objective of this paper is to explain and elucidate the formalism of quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination, and it is shown that it is always possible to choose the inner product that is appropriate for the Hilbert space of physical states.

Faster than Hermitian quantum mechanics.

TLDR
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.

Must a Hamiltonian be Hermitian

A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space–time reflection symmetry (PT

Consistency of PT-symmetric quantum mechanics

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

Experimental quantum cloning in a pseudo-unitary system

Deterministically cloning (copying) nonorthogonal states is forbidden in quantum mechanics, but deterministic pseudo-unitary cloning is possible in a nonunitary system. We prove and show that, for

Introduction to 𝒫𝒯-symmetric quantum theory

In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability

Complex extension of quantum mechanics.

TLDR
If PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian, and this work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
...