Quantum feedback with weak measurements
arXiv:quant-ph/9905064 · doi:10.1103/PhysRevA.62.012307
Abstract
The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schrödinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.
11 pages, TeX, replaced to incorporate suggestions of Asher Peres
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- Constructive control of quantum systems using factorization of unitary operators
- Fast quantum state discrimination with nonlinear PTP channels
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- Phase locking a clock oscillator to a coherent atomic ensemble
- Parameter Estimation with Mixed-State Quantum Computation
- Macroscopic Observables
- Coherent control and feedback cooling in a remotely-coupled hybrid atom-optomechanical system
- Complex chaos in the conditional dynamics of qubits
- Universal quantum data compression via gentle tomography
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- Simulation of complex dynamics of mean-field -spin models using measurement-based quantum feedback control
- Exponential Sensitivity and its Cost in Quantum Physics
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- Cooling and state preparation in an optical lattice via Markovian feedback control
- Quantum Theory of Feedback of Bosonic Gases
- Thermodynamics of Quantum Measurement and the Demon's Arrow of Time
- Advanced-Retarded Differential Equations in Quantum Photonic Systems
- Feedback-stabilized dynamical steady states in the Bose-Hubbard model
- Experimental orthogonalization of highly overlapping quantum states with single photons
- Weakly measured while loops: peeking at quantum states
- Linear optics substituting scheme for multi-mode operations
- Feedback cooled Bose-Einstein condensation: near and far from equilibrium
- Characterizing quantum instruments: from non-demolition measurements to quantum error correction
- Complex chaos in conditional qubit dynamics and purification protocols
- Microwave Quantum Memcapacitor Effect
- Distributed Partial Quantum Consensus of Qubit Networks with Connected Topologies
- Feedback-induced interactive dynamics: unitary but dissipative evolution
- Employing feedback in adiabatic quantum dynamics
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- Weak-Measurement-Induced Heating in Bose-Einstein Condensates
- Feedback control of coherent spin states using weak nondestructive measurements
- Measurement and Memory in the Periodically Driven Complex Ginzburg-Landau equation
- A Nonlinear Journey from Structural Phase Transitions to Quantum Annealing
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- Chaos-Mediated Quantum State Discrimination Near Unit Fidelity
- On the Simulation of Adaptive Measurements via Postselection
- Feedback cooling of fermionic atoms in optical lattices