Coherent versus measurement feedback: Linear systems theory for quantum information
arXiv:1406.6466 · doi:10.1103/PhysRevX.4.041029
Abstract
To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
21 pages, 10 figures, to appear in Physical Review X
References in corpus (46)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Noiseless Quantum Codes
- Quantum interface between light and atomic ensembles
- Real-time quantum feedback prepares and stabilizes photon number states
- Feedback-control of quantum systems using continuous state-estimation
- Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
- Using interference for high fidelity quantum state transfer in optomechanics
- Stabilizing entanglement autonomously between two superconducting qubits
- Coherent quantum LQG control
- Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics
- Continuous quantum error correction via quantum feedback control
- Photon storage in Lambda-type optically dense atomic media. I. Cavity model
- Coherent-feedback quantum control with a dynamic compensator
- All-optical versus electro-optical quantum-limited feedback
- Coherent Quantum-Noise Cancellation for Optomechanical Sensors
- Squeezing Components in Linear Quantum Feedback Networks
- Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
- Feedback cooling of a nanomechanical resonator
- Network Synthesis of Linear Dynamical Quantum Stochastic Systems
- Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction
- Evading quantum mechanics
- Unconditional two-mode squeezing of separated atomic ensembles
- Advantages of Coherent Feedback for Cooling Quantum Oscillators
- Deterministic single photons via conditional quantum evolution
- Three-dimensional theory for interaction between atomic ensembles and free-space light
- Robust quantum parameter estimation: coherent magnetometry with feedback
- Using dark modes for high-fidelity optomechanical quantum state transfer
- Experimental demonstration of coherent feedback control on optical field squeezing
- Preparing a mechanical oscillator in non-Gaussian quantum states
- A discrete invitation to quantum filtering and feedback control
- Enhancement of Field Squeezing Using Coherent Feedback
- Quantum locking of mirrors in interferometers
- Unconditional quantum-noise suppression via measurement-based quantum feedback
- Coherent Cancellation of Backaction Noise in optomechanical Force Measurements
- Tunable coupling to a mechanical oscillator circuit using a coherent feedback network
- Coherent control of single photon states
- Coherent-feedback control strategy to suppress spontaneous switching in ultra-low power optical bistability
- Zero-dynamics principle for perfect quantum memory in linear networks
- Coherent controllers for optical-feedback cooling of quantum oscillators
- Avoiding dissipation in a system of three quantum harmonic oscillators
- Decoherence-free linear quantum subsystems
- Scattering of polarized laser light by an atomic gas in free space: a QSDE approach
- Back-action cancellation in interferometers by quantum locking
- Noise reduction in gravitational wave interferometers using feedback
- Dynamical Gaussian state transfer with quantum error correcting architecture
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- The SLH framework for modeling quantum input-output networks
- Time-delayed quantum feedback control
- Enhanced entanglement of two different mechanical resonators via coherent feedback
- Comparing and combining measurement-based and driven-dissipative entanglement stabilization
- Low-Latency Digital Signal Processing for Feedback and Feedforward in Quantum Computing and Communication
- Hamiltonian identifiability assisted by single-probe measurement
- The Kalman Decomposition for Linear Quantum Systems
- Unitarity, Feedback, Interactions -- Dynamics Emergent from Repeated Measurements
- Analysis and Control of Quantum Finite-level Systems Driven by Single-photon Input States
- Optical coherent feedback control of a mechanical oscillator
- Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: analytical results in the regime of ground-state cooling
- Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model
- Quantum state engineering in hybrid open quantum systems
- Thermodynamics of quantum feedback cooling
- Mesoscopic ultrafast nonlinear optics -- The emergence of multimode quantum non-Gaussian physics
- Quantum feedback amplification
- Dark Modes of Quantum Linear Systems
- A simultaneous feedback and feed-forward control and its application to realize a random walk on the Bloch sphere in a superconducting Xmon-qubit system
- Coherently tracking the covariance matrix of an open quantum system
- Coherent vs. measurement-based feedback for controlling a single qubit
- Coherent feedback in optomechanical systems in the sideband-unresolved regime
- Optimal control of linear Gaussian quantum systems via quantum learning control
- Quantum functionalities via feedback amplification
- Volterra filters for quantum estimation and detection
- Noisy atomic magnetometry with Kalman filtering and measurement-based feedback
- Generating Robust Entanglement via Quantum Feedback
- Pole Placement Approach to Coherent Passive Reservoir Engineering for Storing Quantum Information
- Quantum Fourier transform on photonic qubits using cavity QED
- Replacing measurement feedback with coherent feedback for quantum state preparation
- Ultimate squeezing through coherent quantum feedback: A fair comparison with measurement-based schemes
- The role of quantum measurements in physical processes and protocols
- Non-Markovian Quantum Feedback Networks I: Quantum Transmission Lines, Lossless Bounded Real Property and Limit Markovian Channels
- Non-Markovian Quantum Feedback Networks II: Controlled Flows
- Unified Collision Model of Coherent and Measurement-based Quantum Feedback
- Control limit on quantum state preparation under decoherence
- Feasibility study of a coherent feedback squeezer
- Quantum limits on detection sensitivity of a linear detector with feedback
- Efficient inference of quantum system parameters by Approximate Bayesian Computation