Qubit state monitoring by measurement of three complementary observables

Abstract

We consider the evolution of a spin 1/2 (qubit) under the simultaneous continuous measurement of three non-commuting qubit operators sigma_x, sigma_y, sigma_z. For identical ideal detectors the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.

arXiv comment5 pages, 4 figures

References in corpus (16)

• Introduction to Quantum Noise, Measurement and Amplification
• Quantum jumps of light recording the birth and death of a photon in a cavity
• Experimental violation of a Bell's inequality in time with weak measurement
• Uncollapsing of a quantum state in a superconducting phase qubit
• Selective quantum evolution of a qubit state due to continuous measurement
• How to project qubits faster using quantum feedback
• Quantum feedback control of a solid-state qubit
• Quantum error correction for continuously detected errors
• Entanglement of solid-state qubits by measurement
• Signatures of quantum behavior in single-qubit weak measurements
• Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian analysis
• Continuous quantum measurement with independent detector cross-correlations
• Reconsidering Rapid Qubit Purification by Feedback
• Statistics of Measurement of Non-commuting Quantum Variables: Monitoring and Purification of a qubit
• Quantum Superposition State Production by Continuous Observations and Feedback
• Replacing Quantum Feedback with Open-Loop Control and Quantum Filtering

Cited by in corpus (29)

• Dynamics of simultaneously measured non-commuting observables
• Action principle for continuous quantum measurement
• Spin dynamics in a strongly driven system: very slow Rabi oscillations
• Engineering arbitrary pure and mixed quantum states
• Non-Markovian quantum input-output networks
• Continuous quantum nondemolition measurement of the transverse component of a qubit
• Simultaneous continuous measurement of non-commuting observables: quantum state correlations
• Simultaneous measurement of two non-commuting quantum variables: Solution of a dynamical model
• Stochastic Path Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator
• Simultaneous weak measurement of non-commuting observables
• Probing quantumness with joint continuous measurements of non-commuting qubit observables
• Qubit purification speed-up for three complementary continuous measurements
• Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
• Linear feedback stabilization of a dispersively monitored qubit
• Von Neumann spin measurements with Rashba fields
• Multi-time correlators in continuous measurement of qubit observables
• Estimation of classical parameters via continuous probing of complementary quantum observables
• Practical Few-Atom Quantum Reservoir Computing
• Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
• Bacon-Shor code with continuous measurement of non-commuting operators
• Past observable dynamics of a continuously monitored qubit
• How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$
• Correlators exceeding one in continuous measurements of superconducting qubits
• Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups
• Memory effects in a sequence of measurements of non-commuting observables
• Detector dependency of diffusive quantum monitorings
• Probability distributions of continuous measurement results for two non-commuting variables and conditioned quantum evolution
• Quantum feedback for measurement and control
• Einselection from incompatible decoherence channels