PT-symmetric quantum state discrimination

Abstract

Suppose that a system is known to be in one of two quantum states, $|{\psi }_1>$ or $|{\psi }_2>$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states, it is always possible to choose this inner product so that the two states $|{\psi }_1>$ and $|{\psi }_2>$ are orthogonal. Thus, quantum state discrimination can, in principle, be achieved with a single measurement.

4 pages, no figures

References in corpus (9)

• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Faster than Hermitian Quantum Mechanics
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• The Naimark dilated PT-symmetric brachistochrone
• Observation of Fast Evolution in Parity-Time-Symmetric System
• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• The quantum brachistochrone problem for non-Hermitian Hamiltonians

Cited by in corpus (19)

• Local PT symmetry violates the no-signaling principle
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Quantum simulation of parity-time symmetry breaking with a superconducting quantum processor
• Experimental observation of information flow in the anti-$\mathcal{P}\mathcal{T}$-symmetric system
• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Quantum state discrimination in a PT-symmetric system
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Observing a Changing Hilbert-Space Inner Product
• Quantum deleting and cloning in a pseudo-unitary system
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• Temporal correlation beyond quantum bounds in non-hermitian dynamics
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• The role of singular values in entanglement distillation and unambiguous state discrimination
• Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians
• Chaos-Mediated Quantum State Discrimination Near Unit Fidelity
• Interaction without back-action in the context of quantum manipulation
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory