Fundamental quantum limits in optical metrology from rate-distortion theory
arXiv:1204.3761 · doi:10.1088/1751-8121/aade9f
Abstract
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit classical information of various optical channels specified by the system design. The bounds are expressed in terms of the system parameters, the prior probability distribution of the parameter, and the average energy, i.e., number of photons in the probe state. For phase estimation, the bounds pertain to a cyclic mean squared error criterion incorporating the cyclic nature of the phase. In the absence of optical loss, our bounds are applicable to multimode linear phase modulation schemes (including ancilla-assisted ones), and to nonlinear modulations on a single mode. The bounds display inverse-quadratic Heisenberg-limit scaling of the cyclic mean square error with respect to . In the presence of any finite amount of loss, a lower bound on ancilla-assisted phase estimation with standard-quantum-limit (SQL) scaling is derived, which is shown to be little different from a similar bound for coherent-state probes. For systems involving a single optical mode, we also obtain lower bounds on the mean squared error of estimating any classical parameter, and on the average error probability of any -ary communication system under an average energy constraint. The bounds are valid for arbitrary quantum measurements, for any prior probability distribution, and do not rely on unbiasedness assumptions.
15 pages, 6 figures; approximates published version. Improved presentation, updated references and added new results on multimode multipass phase estimation, -ary optical communication, and general single-mode estimation. The bounds for phase estimation are now in terms of the cyclic mean squared error criterion
References in corpus (28)
- Quantum sensing
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum metrology from a quantum information science perspective
- The elusive Heisenberg limit in quantum enhanced metrology
- Entanglement-free Heisenberg-limited phase estimation
- Quantum limits in optical interferometry
- From Classical to Quantum Shannon Theory
- Compatibility in Multiparameter Quantum Metrology
- Entanglement-enhanced measurement of a completely unknown phase
- Phase matching condition for enhancement of phase sensitivity in quantum metrology
- A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
- Ziv-Zakai Error Bounds for Quantum Parameter Estimation
- Phase estimation without a priori knowledge in the presence of loss
- Quantum metrology with open dynamical systems
- Quantum limits in the measurement of very small displacements in optical images
- Sub-Heisenberg estimation strategies are ineffective
- The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
- Does nonlinear metrology offer improved resolution? Answers from quantum information theory
- Universality of the Heisenberg limit for estimates of random phase shifts
- Quantum measurement bounds beyond the uncertainty relations
- Quantum rate distortion, reverse Shannon theorems, and source-channel separation
- Sub-Heisenberg estimation of non-random phase-shifts
- Quantum Metrological Bounds for Vector Parameter
- Optimal Quantum States for Image Sensing in Loss
- Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
- The entropy gain of infinite-dimensional quantum channels
- Symmetric M-ary phase discrimination using quantum-optical probe states
- Joint estimation of phase and phase diffusion for quantum metrology