Optimal detection of quantum states via projective measurements

Abstract

We consider the quantum dynamical evolution of a fully-connected quantum system subjected to random projective measurements and study the first detection time of an extended subspace of the Hilbert space. Exact analytical expressions are obtained for the mean first detection time and the full first detection probability distribution as functionals of the initial state $|{\psi }_0⟩$ and the measurement rate $r$. Exact enumeration agrees perfectly with our analytical predictions.

arXiv comment43 pages, 5 figures

References in corpus (52)

• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• Quantum walks: a comprehensive review
• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Run and tumble particle under resetting: a renewal approach
• Diffusion in a potential landscape with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Diffusion with resetting in arbitrary spatial dimension
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Fluctuating interfaces subject to stochastic resetting
• Hitting time for quantum walks on the hypercube
• Recurrence for discrete time unitary evolutions
• Monotonous continuous-time random walks with drift and stochastic reset events
• Scaled Brownian motion with renewal resetting
• Quantum dynamics with stochastic reset
• Quantum walks with infinite hitting times
• Detection of a quantum particle on a lattice under repeated projective measurements
• First detected arrival of a quantum walker on an infinite line
• Spectral properties of simple classical and quantum reset processes
• Sisyphus random walk
• Restart expedites quantum walk hitting times
• A Review on Quantum Search Algorithms
• Stochastic resetting in interacting particle systems: A review
• Hitting time for the continuous quantum walk
• Large fluctuations of the first detected quantum return time
• Spatial search by continuous-time quantum walks on crystal lattices
• Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit
• Quantum Renewal Equation for the first detection time of a quantum walk
• Return to origin problem for particle on a one-dimensional lattice with quasi-Zeno dynamics
• Dark states of quantum search cause imperfect detection
• Emergent quantum correlations and collective behavior in non-interacting quantum systems subject to stochastic resetting
• Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain
• First detection probability in quantum resetting via random projective measurements
• Measurement induced quantum walks on an IBM Quantum Computer
• The first detection time of a quantum state under random probing
• Generating Entanglement by Quantum Resetting
• Quantum resetting in continuous measurement induced dynamics of a qubit
• Instability in the quantum restart problem
• Dynamics of closed quantum systems under stochastic resetting
• Stochastic resets in the context of a tight-binding chain driven by an oscillating field
• Dynamically emergent correlations in bosons via quantum resetting
• Thermodynamic phases in first detected return times of quantum many-body systems
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Interaction-induced transition in quantum many-body detection probability
• Dynamically generated correlations in a trapped bosonic gas via frequency quenches
• First-detection-time statistics in many-body quantum transport