Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian analysis

Abstract

The informational approach to continuous quantum measurement is derived from POVM formalism for a mesoscopic scattering detector measuring a charge qubit. Quantum Bayesian equations for the qubit density matrix are derived, and cast into the form of a stochastic conformal map. Measurement statistics are derived for kicked quantum nondemolition measurements, combined with conditional unitary operations. These results are applied to derive a feedback protocol to produce an arbitrary pure state after a weak measurement, as well as to investigate how an initially mixed state becomes purified with and without feedback.

13 pages, 3 figures

References in corpus (39)

• Single-shot read-out of an individual electron spin in a quantum dot
• Scattering approach to parametric pumping
• Coherent manipulation of electronic states in a double quantum dot
• Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field
• Few-Electron Quantum Dot Circuit with Integrated Charge Read-Out
• Manipulation of a single charge in a double quantum dot
• Charge-qubit operation of an isolated double quantum dot
• Measurements with a noninvasive detector and dephasing mechanism
• Continuous quantum measurement of a double dot
• Selective quantum evolution of a qubit state due to continuous measurement
• Continuous weak measurement of quantum coherent oscillations
• Dephasing and the Orthogonality Catastrophe in Tunneling through a Quantum Dot: the ``Which Path?'' Interferometer
• Geometry, Statistics and Asymptotics of Quantum Pumps
• Dephasing in a quantum dot due to coupling with a quantum point contact
• Quantum-Limited Measurement and Information in Mesoscopic Detectors
• Efficiency of Mesoscopic Detectors
• Dynamics of a mesoscopic qubit under continuous quantum measurement
• Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback
• How to project qubits faster using quantum feedback
• Leggett-Garg inequality with a kicked quantum pump
• Quantum feedback control of a solid-state qubit
• Charge Fluctuations in Quantum Point Contacts and Chaotic Cavities in the Presence of Transport
• Direct control of the tunnel splitting in a one-electron double quantum dot
• Counting statistics and detector properties of quantum point contacts
• Floquet scattering theory for current and heat noise in large amplitude adiabatic pumps
• Continuous quantum measurement with independent detector cross-correlations
• Rapid Ballistic Readout for Flux Qubits
• Charge Relaxation and Dephasing in Coulomb Coupled Conductors
• Reconsidering Rapid Qubit Purification by Feedback
• Quantum Nondemolition Measurement of a Kicked Qubit
• Quantum nondemolition measurements of a qubit
• Coulomb induced positive current-current correlations in normal conductors
• Probe-configuration dependent dephasing in a mesoscopic interferometer
• Nonideal quantum detectors in Bayesian formalism
• Noise and Measurement Efficiency of a Partially Coherent Mesoscopic Detector
• Output spectrum of a measuring device at arbitrary voltage and temperature
• Quantum trajectories for the realistic measurement of a solid-state charge qubit
• Optimal feedback control for the rapid preparation of a single qubit
• Density matrix purification due to continuous quantum measurement

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• Stochastic path integral formalism for continuous quantum measurement
• Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions
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• Thermal transistor and thermometer based on Coulomb-coupled conductors
• Qubit state monitoring by measurement of three complementary observables
• Resonant Scattering Can Enhance the Degree of Entanglement
• Rapid Measurement of Quantum Systems using Feedback Control
• Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation
• Daemonic ergotropy in continuously-monitored open quantum batteries
• Quantum trajectories and their statistics for remotely entangled quantum bits
• Anatomy of Fluorescence: Quantum trajectory statistics from continuously measuring spontaneous emission
• Weak measurement and control of entanglement generation
• Parity detection and entanglement with a Mach-Zehnder interferometer
• Rapid estimation of drifting parameters in continuously measured quantum systems
• Quantum instruments as a foundation for both states and observables
• Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
• Models of mesoscopic time-resolved current detection
• Phase transitions in sequential weak measurements
• Entropic Updating of Probability and Density Matrices
• Crossover of phase qubit dynamics in presence of negative-result weak measurement
• Implementation schemes for unsharp measurements with trapped ions
• Quantum nondemolition-like, fast measurement scheme for a superconducting qubit
• Quantum rifling: protecting a qubit from measurement back-action
• Characterizing a statistical arrow of time in quantum measurement dynamics
• Qubit purification speed-up for three complementary continuous measurements
• Weak measurement and rapid state reduction in bipartite quantum systems
• Linear feedback stabilization of a dispersively monitored qubit
• Weak measurement of quantum dot spin qubits
• On-demand maximally entangled states with a parity meter and continuous feedback
• Continuous measurement of a qudit using dispersively coupled radiation
• Sequential generalized measurements: Asymptotics, typicality and emergent projective measurements
• Rapid-purification protocols for optical homodyning
• Quantum error correction using weak measurements
• Readout of solid-state charge qubits using a single-electron pump
• The Inferential Design of Entropy and its Application to Quantum Measurements
• Optimal measurement-based feedback control for a single qubit: a candidate protocol
• Artificially intelligent Maxwell's demon for optimal control of open quantum systems
• Rapid readout of a register of qubits using open loop quantum control
• Phase Diagram of the Dynamics of a Precessing Qubit under Quantum Measurement
• Daemonic ergotropy of Gaussian quantum states and the role of measurement-induced purification via general-dyne detection
• Assessing the quantumness of the annealing dynamics via Leggett Gargs inequalities: a weak measurement approach