Generating nonlinearities from conditional linear operations, squeezing and measurement for quantum computation and super-Heisenberg sensing

Abstract

Large optical nonlinearities can have numerous applications, ranging from the generation of cat-states for optical quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources. However, the generation of ultra-large optical nonlinearities has proved immensely challenging experimentally. We describe a novel protocol where one can effectively generate large optical nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the probe mode. Our protocol can generate high quality optical Schr{ö}dinger cat states useful for optical quantum computing and can be used to perform sensing of an unknown rotation or displacement in phase space, with super-Heisenberg scaling in the resources. We finally describe a potential experimental implementation using atomic ensembles interacting with optical modes via the Faraday effect.

arXiv comment18 pages, 9 figures. New in this version: typos fixed. Fixed order of subfigs in Fig. 2

References in corpus (35)

• Decoherence, einselection, and the quantum origins of the classical
• Advances in Quantum Metrology
• Quantum metrology with nonclassical states of atomic ensembles
• Nonlinear atom interferometer surpasses classical precision limit
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Observation of quantum state collapse and revival due to the single-photon Kerr effect
• Generalized Limits for Single-Parameter Quantum Estimation
• Weak nonlinearities: A new route to optical quantum computation
• Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
• Quantum Metrology: Dynamics vs. Entanglement
• Graphical calculus for Gaussian pure states
• Weak force detection with superposed coherent states
• Quantum computing with rotation-symmetric bosonic codes
• Optimal phase measurements with pure Gaussian states
• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Quantum-limited metrology with product states
• Quantum control and measurement of atomic spins in polarization spectroscopy
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Nonlinear quantum metrology of many-body open systems
• Quantum limits on post-selected, probabilistic quantum metrology
• Quantum metrology for non-linear phase shifts with entangled coherent states
• Nonlinear quantum metrology using coupled nanomechanical resonators
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
• Ultimate limits for quantum magnetometry via time-continuous measurements
• Quantum metrology at the Heisenberg limit with ion traps
• Nonlinear metrology with a quantum interface
• Simulating nonlinear dynamics of collective spins via quantum measurement and feedback
• Ultrasensitive Atomic Spin Measurements with a Nonlinear Interferometer
• Sub-Heisenberg-limited nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound
• Nonlinear Michelson interferometer for improved quantum metrology
• The phase sensitivity of a fully quantum three-mode nonlinear interferometer
• Nonlinear fiber gyroscope for quantum metrology
• Improving quantum parameter estimation by monitoring quantum trajectories

Cited by in corpus (5)

• Quantum metrology in the noisy intermediate-scale quantum era
• All-optical quantum computing using cubic phase gates
• Lowering Helstrom Bound with non-standard coherent states
• Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit
• Optimal quantum sensing of the nonlinear bosonic interactions using Fock states