Statistics of Measurement of Non-commuting Quantum Variables: Monitoring and Purification of a qubit
arXiv:cond-mat/0703344 · doi:10.1103/PhysRevB.78.045308
Abstract
We address continuous weak linear quantum measurement and argue that it is best understood in terms of statistics of the outcomes of the linear detectors measuring a quantum system, for example, a qubit. We mostly concentrate on a setup consisting of a qubit and three independent detectors that simultaneously monitor three noncommuting operator variables, those corresponding to three pseudospin components of the qubit. We address the joint probability distribution of the detector outcomes and the qubit variables. When analyzing the distribution in the limit of big values of the outcomes, we reveal a high degree of correspondence between the three outcomes and three components of the qubit pseudospin after the measurement. This enables a high-fidelity monitoring of all three components. We discuss the relation between the monitoring described and the algorithms of quantum information theory that use the results of the partial measurement. We develop a proper formalism to evaluate the statistics of continuous weak linear measurement. The formalism is based on Feynman-Vernon approach, roots in the theory of full counting statistics, and boils down to a Bloch-Redfield equation augmented with counting fields.
30 pages, 5 figures
References in corpus (24)
- Quantum Cryptography
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Quantum state engineering with Josephson-junction devices
- Quantum privacy amplification and the security of quantum cryptography over noisy channels
- Electron Counting Statistics and Coherent States of Electric Current
- Heisenberg's Uncertainty Principle
- Measurements with a noninvasive detector and dephasing mechanism
- Continuous quantum measurement of a double dot
- Undoing a weak quantum measurement of a solid-state qubit
- Quantum non-demolition measurement of a superconducting two-level system
- Recipes for spin-based quantum computing
- Full counting statistics of a general quantum mechanical variable
- Quantum-Limited Measurement and Information in Mesoscopic Detectors
- Efficiency of Mesoscopic Detectors
- Measurement quantum mechanics and experiments on quantum Zeno effect
- Purification through Zeno-like Measurements
- Statistics and noise in a quantum measurement process
- Rapid Ballistic Readout for Flux Qubits
- Continuous quantum measurement with independent detector cross-correlations
- Reading-out the state of a flux qubit by Josephson transmission line solitons
- Feedback of the electromagnetic environment on current and voltage fluctuations out of equilibrium
- Using Qubits to Measure Fidelity in Mesoscopic Systems
- Full Counting Statistics of Cooper Pair Shuttling
- Full Counting Statistics of Non-Commuting Variables: the Case of Spin Counts
Cited by in corpus (24)
- Action principle for continuous quantum measurement
- Weak measurement protocols for Majorana bound state identification
- Stochastic path integral formalism for continuous quantum measurement
- Negative Full Counting Statistics Arise From Interference Effects
- Qubit state monitoring by measurement of three complementary observables
- Effects of Quantum Coherence on Work Statistics
- Tomography of many-body weak values: Mach-Zehnder interferometry
- Proposal for a cumulant-based Bell test for mesoscopic junctions
- Weak and strong measurement of a qubit using a switching-based detector
- The information about the state of a qubit gained by a weakly coupled detector
- Simultaneous continuous measurement of non-commuting observables: quantum state correlations
- Approximate joint measurement of qubit observables through an Arthur-Kelly type model
- Qubit purification speed-up for three complementary continuous measurements
- Bacon-Shor code with continuous measurement of non-commuting operators
- Practical Few-Atom Quantum Reservoir Computing
- How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of
- Decoherence effects on weak value measurements in double quantum dots
- Probability distributions of continuous measurement results for conditioned quantum evolution
- Weak values under uncertain conditions
- Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups
- Estimating the reduction time of quantum states
- Modified Kubo formula with a complex force term for weak measurement
- Probability distributions of continuous measurement results for two non-commuting variables and conditioned quantum evolution
- On the role of the measurement apparatus in quantum measurements