Stephen M. Barnett, David T. Pegg, John Jeffers, Ottavia Jedrkiewicz
Measurement of a quantum system provides information concerning the state in which it was prepared. In this paper we show how the retrodictive formalism can be used to evaluate the probability associated with any one of a given set of preparation events. We illustrate our method by calculating the retrodictive density operator for a two-level atom coupled to the electromagnetic field.
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In the Jaynes-Cummings model a two-level atom interacts with a single-mode electromagnetic field. Quantum mechanics predicts collapses and revivals in the probability that a measurement will show the atom to be excited at various times after the initial preparation of the atom and field. In retrodictive quantum mechanics we seek the probability that the atom was prepared in a particular state given the initial state of the field and the outcome of a later measurement on the atom. Although this is not simply the time reverse of the usual predictive problem, we demonstrate in this paper that ret…
Quantum measurement retrodiction and entropic uncertainty relations
本文提出基于最小变化原理的量子测量反推方法，推导出与散度无关的量子贝叶斯反推，并建立两个反推熵不确定性关系，适用于广泛测量和态类别。
We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalised probability operator measure element associated with the result. We examine applications to quantum optical cryptography and to the optical beam splitter.
We use retrodictive quantum theory to describe cavity field measurements by successive atomic detections in the micromaser. We calculate the state of the micromaser cavity field prior to detection of sequences of atoms in either the excited or ground state, for atoms that are initially prepared in the excited state. This provides the POM elements, which describe such sequences of measurements.
Irreversibility is usually captured by a comparison between the process that happens and a corresponding "reverse process". In the last decades, this comparison has been extensively studied through fluctuation relations. Here we revisit fluctuation relations from the standpoint, suggested decades ago by Watanabe, that the comparison should involve the prediction and the retrodiction on the unique process, rather than two processes. We identify a necessary and sufficient condition for a retrodictive reading of a fluctuation relation. The retrodictive narrative also brings to the fore the possib…
Quantum retrodiction in Gaussian systems and applications in optomechanics
该研究介绍量子态反演的通用框架及高斯系统的实用公式，将其应用于光力学系统，表征了可实现的反演POVM，证实近理想测量机械振荡器正交分量的可行性，为破坏性量子态层析成像奠基。
Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with the a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper we show how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optica…
A Retrodictive Approach to Quantum State Smoothing
针对量子态平滑中非物理结果和环境测量假设不可验证的问题，本文提出基于量子贝叶斯回溯推断的平滑态定义，保证物理性、无需环境假设并提升平均纯度。
Unifying Quantum Smoothing Theories with Extended Retrodiction
通过引入扩展先验，将量子状态平滑统一为基于贝叶斯回溯的框架，揭示不同方法的本质联系并给出信息论刻画。
Quantifying Measurement Objectivity: A Retrodictive Approach
该研究针对量子测量结果何时可解读为揭示预先存在的客观属性的问题，提出基于量子测量回溯预测的定量方法，构造量化非客观性的双线性型并证明其分解性质，得出总非客观性在特定映射下不降低的结论。
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. We here use quantum retrodiction to produce a rigorous refinement of the theory put forward in Phys. Rev. E {\bf 83}, 056118 (2011). We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte-Carlo simulatio…
Quantitative studies of irreversibility in statistical mechanics often involve the consideration of a reverse process, whose definition has been the object of many discussions, in particular for quantum mechanical systems. Here we show that the reverse channel very naturally arises from Bayesian retrodiction, both in classical and quantum theories. Previous paradigmatic results, such as Jarzynski's equality, Crooks' fluctuation theorem, and Tasaki's two-measurement fluctuation theorem for closed driven quantum systems, are all shown to be consistent with retrodictive arguments. Also, various c…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric postulate is presented, from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. It is shown that the new postulate is perfectly consistent with the conventional postulate.
This thesis is concerned with retrodiction and measurement in quantum optics. The latter of these two concepts is studied in particular form with a general optical multiport device, consisting of an arbitrary array of beam-splitters and phase-shifters. I show how such an apparatus generalizes the original projection synthesis technique, introduced as an in principle technique to measure the canonical phase distribution. Just as for the original projection synthesis, it is found that such a generalised device can synthesize any general projection onto a state in a finite dimensional Hilbert spa…
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturban…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for the prediction of "hypothetical future measurements", and it does not describe the situation where knowledge is available about the system both earlier and later than the time of the measurement. We study what happens under such circumstances with an atomic ensemble containing $10^{11}$ $^{87}\text{Rb}$ atoms, initiated nearly in the ground state in presence …
Continuous field tracking with machine learning and steady state spin squeezing
本文结合光泵浦与连续量子非破坏测量，在热原子系综中实现约一天、-3.23 dB的稳态自旋压缩，并利用深度学习解码光信号以追踪连续波动磁场，在原子磁强计中验证了量子增强。
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