Repeatability of measurements: Equivalence of hermitian and non-hermitian observables

Abstract

A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Therefore, even a possibility to describe physical reality by means of non-hermitian operators should \emph{volens nolens} be excluded as their eigenstates are not orthogonal. Here, we show that non-hermitian operators with real spectrum can be treated within the standard framework of quantum mechanics. Furthermore, we propose a quantum canonical transformation that maps hermitian systems onto non-hermitian ones. Similar to classical inertial forces this transformation is accompanied by an energetic cost pinning the system on the unitary path.

References in corpus (13)

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Cited by in corpus (9)

• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Fundamentals of Quantum Mechanics in Liouville Space
• $\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence
• Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality
• Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals
• Composite quantum Coriolis forces
• Broken Hermiticity phase transition in Bose-Hubbard model
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Qubit: Decoherence and Entanglement Entropy