Simultaneous continuous measurement of non-commuting observables: quantum state correlations
arXiv:1706.09670 · doi:10.1103/PhysRevA.97.012118
Abstract
We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories, which has the same fixed initial state and can also be optionally constrained by a fixed final state. We develop a stochastic path integral description for the continuous quantum measurement and use it to calculate the considered correlators. Exact analytic results are possible in the case of ideal measurements of equal strength and are also shown to agree with solutions obtained using the Fokker-Planck equation. For a more general case with decoherence effects and inefficiency, we use a diagrammatic approach to find the correlators perturbatively in the quantum efficiency. We also calculate the state correlators for the quantum trajectories which are extracted from readout signals measured in a transmon qubit experiment, by means of the quantum Bayesian state update. We find an excellent agreement between the correlators based on the experimental data and those obtained from our analytical and numerical results.
arXiv comment12 pages, 4 figures
References in corpus (25)
- Real-time quantum feedback prepares and stabilizes photon number states
- A Straightforward Introduction to Continuous Quantum Measurement
- Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
- Observing single quantum trajectories of a superconducting qubit
- Experimental violation of a Bell's inequality in time with weak measurement
- Deterministic entanglement of superconducting qubits by parity measurement and feedback
- Continuous quantum measurement of a double dot
- Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits
- Quantum back-action of variable-strength measurement
- Selective quantum evolution of a qubit state due to continuous measurement
- Dynamics of simultaneously measured non-commuting observables
- How to project qubits faster using quantum feedback
- Quantum feedback control of a solid-state qubit
- Observing interferences between past and future quantum states in resonance fluorescence
- Entanglement of solid-state qubits by measurement
- Action principle for continuous quantum measurement
- Reversing quantum trajectories with analog feedback
- Continuous quantum measurement with independent detector cross-correlations
- Decoherence and the theory of continuous quantum measurements
- Stochastic path integral formalism for continuous quantum measurement
- Qubit state monitoring by measurement of three complementary observables
- Quantum trajectories and their statistics for remotely entangled quantum bits
- Anatomy of Fluorescence: Quantum trajectory statistics from continuously measuring spontaneous emission
- Statistics of Measurement of Non-commuting Quantum Variables: Monitoring and Purification of a qubit
- Correlators in simultaneous measurement of non-commuting qubit observables
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- Chaos in Continuously Monitored Quantum Systems: An Optimal Path Approach
- Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
- Thermodynamics of Quantum Measurement and the Demon's Arrow of Time
- Multi-time correlators in continuous measurement of qubit observables
- Quantum polyspectra for modeling and evaluating quantum transport measurements: A unifying approach to the strong and weak measurement regime
- Quantum dynamics under simultaneous and continuous measurement of noncommutative observables
- 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
- Noise-assisted and monitoring-enhanced quantum bath tagging
- Application of simultaneous and continuous measurement of noncommutative observables: Preparation of the pure ideal quadrature-squeezed state by feedback control