Retrodiction beyond the Heisenberg uncertainty relation

Squeezed light from an oscillator measured at the rate of oscillation

Sufficiently fast continuous measurements of the position of an oscillator approach measurements projective on position eigenstates. We evidence the transition into the projective regime for a spin oscillator within an ensemble of 2 × 1010 room-temperature atoms by observing correlations between the quadratures of the meter light field. These correlations squeeze the fluctuations of one light quadrature below the vacuum level. When the measurement is slower than the oscillation, we generate 11 . 5 - 1.5 + 2.5 dB and detect 8 . 5 - 0.1 + 0.1 dB of squeezing in a tunable band that is a fraction of the resonance frequency. When the measurement is as fast as the oscillation, we detect 4.7 dB of squeezing that spans more than one decade of frequencies below the resonance. Our results demonstrate a new regime of continuous quantum measurements on material oscillators, and set a new benchmark for the performance of a linear quantum sensor.

Prediction-Retrodiction Measurements for Teleportation and Conditional State Transfer

Regular measurements allow predicting the future and retrodicting the past of quantum systems. Time-nonlocal measurements can leave the future and the past uncertain, yet establish a relation between them. We show that continuous time-nonlocal measurements can be used to transfer a quantum state via teleportation or direct transmission. Considering two oscillators probed by traveling fields, we analytically identify strategies for performing the state transfer perfectly across a wide range of linear oscillator-field interactions beyond the pure beam-splitter and two-mode-squeezing types.

Quantum Retrodiction: Foundations and Controversies

Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum retrodiction and highlight its intimate connection with the Bayesian interpretation of probability. The close link with Bayesian methods enables us to explore controversies and misunderstandings about retrodiction that have appeared in the literature. To be clear, quantum retrodiction is universally applicable and draws its validity directly from conventional predictive quantum theory coupled with Bayes’ theorem.