The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful post-selection. %% In this work we show that, rather than the Gaussian meter state as typically considered, using the optical coherent state as a meter, the WVA measurement can definitely outperform the conventional measurement not involving the strategy of post-selection. %% We also show that the post-selection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in sharp contrast to the claim proved in the absence of post-selection. The post-selection strategy can also result in the precision of Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but without using any expensive quantum resources. %% The present work may stimulate further investigations for the potential of the post-selection strategy in quantum precision measurements.
Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models can account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case …
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half syst…
We show that postselection offers a nonclassical advantage in metrology. In every parameter-estimation experiment, the final measurement or the postprocessing incurs some cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from an experimental trial) to cost. This improvement, we show, stems from the negativity of a quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution can be expressed as real and nonnegati…
The purport of quantum teleportation is to completely transfer information from one party to another distant partner. However, from the perspective of parameter estimation, it is the information carried by a particular parameter, not the information of total quantum state that needs to be teleported. Due to the inevitable noise in environment, we propose two schemes to enhance quantum Fisher information (QFI) teleportation under amplitude damping noise with the technique of partial measurements. We find that post partial measurement can greatly enhance the teleported QFI, while the combination…
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising resu…
In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum c…
We study the interrelationships between the Fisher information metric recently introduced, on the basis of maximum entropy considerations, by Brody and Hughston (quant-ph/9906085) and the monotone metrics, as explicated by Petz and Sudar. This new metric turns out to be not strictly monotone in nature, and to yield (via its normalized volume element) a prior probability distribution over the Bloch ball of two-level quantum systems that is less noninformative than those obtained from any of the monotone metrics, even the minimal monotone (Bures) metric. We best approximate the additional inform…
In this paper we provide the answer to the following question: given an arbitrary pure input state and a general, unbalanced, Mach-Zehnder interferometer, what transmission coefficient of the first beam splitter maximizes the quantum Fisher information (QFI)? We consider this question for both single- and two-parameter QFI, or, in other words, with or without having access to an external phase reference. We give analytical results for all involved scenarios. It turns out that, for a large class of input states, the balanced (50/50) scenario yields the optimal two-parameter QFI, however this is…
In probabilistic quantum metrology, one aims at finding weak measurements that concentrate the Fisher Information on the resulting quantum states, post-selected according to the weak outcomes. Though the Quantum Cramér-Rao bound itself cannot be overshot this way, it could be possible to improve the information-cost ratio, or even the total Fisher Information. We propose a post-selection protocol achieving this goal based on single-photon subtraction onto a thermal state of radiation yielding a greater information-cost ratio for the temperature parameter with respect to the standard strategy r…
A recent quantum protocol for counterfactual communication [Y. Aharonov and L. Vaidman, Phys. Rev. A 99, 010103(R), 2019] relies on post-selection to eliminate the weak trace in the transmission channel. We show that the post-selection in this protocol also eliminates the flow of Fisher information from transmitter to receiver. However, we also show that a classical communication protocol with post-selection can be counterfactual. Hence, we argue that post-selection should not be allowed in genuine counterfactual communication. In the quantum counterfactual communication protocol, the probabil…
The technical merits of weak value amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak value amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which uses all of them). Using the Fisher information metric, we demonstrate that weak value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time corre…
For a given metric $g_{μν}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for physical systems, and calculate the probability distribution by optimizing the Fisher information metric under specified constraints. Accordingly, we get differential equations for the probability distributions.
School of Physics, Trinity College Dublin（都柏林三一学院物理学院）；Trinity Quantum Alliance（都柏林量子联盟）；Department of Physics and Astronomy, University of Rochester（罗切斯特大学物理与天文学系）
In this study, we give a new proposal to measure the temperature of the spin in a sample in magnetic resonance force microscopy system by using postselected weak measurement, and investigate the fisher information to estimate the precision of our scheme. We showed that in high temperature regime the temperature of the spin can be measured via weak measurement technique with proper postselection and our scheme able to increase the precision of temperature estimation.
Phase-Driven Precision Boost in Quantum Compression for Postselected Metrology
Novosibirsk State University（新西伯利亚国立大学）；Institute of Automation and Electrometry SBRAS（俄罗斯科学院西伯利亚分院自动化与电磁学研究所）；Lattakia University（拉塔基亚大学）；Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究所）
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.
QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（香港大学计算与数据科学学院量子信息与计算倡议）；Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）
An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities calculated from the proposed state agree with previous expressions, for cases where they both apply. The same probabilities are found when they are calculated in the forward- or reverse-time directions. This work was prompted by several problems raised by Shimony recently in relation to the state, and time symmetry, of pre- and post-selected ensembles.
We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information. Although the signal-to-noise ratio is known to be simply related to the Fisher information under idealised detection, we find the two measures of precision differ markedly for a split detector. We show that a greater signal-to-noise ratio 'before' the detector leads to a greater information penalty, unless adaptive realignment is used. We find that with an …
It is known that weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment, implies the possibility to estimate a very small parameter using the weak measurement technique. But does the weak measurement really bring about the increase of "information" for parameter estimation? This paper clarifies that, in a general situation, the answer is NO; more precisely, the weak measurement cannot further decrease the lower bound of the estimation …
The implementation of weak-value amplification requires the pre- and post-selection of states of a quantum system, followed by the observation of the response of the meter, which interacts weakly with the system. Data acquisition from the meter is conditioned to successful post-selection events. Here we derive an optimal post-selection procedure for estimating the coupling constant between system and meter, and show that it leads both to weak-value amplification and to the saturation of the quantum Fisher information, under conditions fulfilled by all previously reported experiments on the amp…
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering…
We show first reconstructions of the photon-number distribution obtained with a multi-channel fiber-loop detector. Apart from analyzing the statistics of light pulses this device can serve as a sophisticated postselection device for experiments in quantum optics and quantum information. We quantify its efficiency by means of the Fisher information and compare it to the efficiency of the ideal photodetector.
Reshaping nonclassical properties and metrological performance of entangled coherent states via post-selected von Neumann measurements
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所）；Center of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术研究中心）；Wolfram Research South America（Wolfram Research 南美分部）；School of Physics, Liaoning University（辽宁大学物理学院）
In this work, the measurement transition as well as precision measurement advantages of single-photon-added coherent state after postselected von Neumann measurement are investigated. We noticed that the weak-to-strong measurement transition characterized by the shifts of pointer's position and momentum variables occurred in continuously by controlling a dimensionless parameter associated with system-pointer coupling. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected measurements, and the latter is used to find the quantum Fisher information. We found…
A weak value is an effective description of the influence of a pre and post-selected 'principal' system on another 'meter' system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and deflections in otherwise unperturbed variables: this motivates investigation of the potential benefits of the protocol in precision metrology. We present a visual interpretation of weak value experiments in phase space, enabling an evaluation of the effects of three types of detector noise as 'Fisher information efficiency' functions. These functions depend on the…
The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We study the task of estimating unknown parameters encoded in a channel in the sequential setting. A sequential strategy is the most general way to use a channel multiple times. Our goal is to establish lower bounds (called Cramer-Rao bounds) on the estimation error. The bounds we develop are universally applicable; i.e., they apply to all permissible quantum dynamics. We consider the use of catalysts to enhance the power of a channel estimation strategy. This is termed amortization.…
$\mathcal{O}(n)$ alternative to Quantum Fourier Transform with efficient neural net classical post-processing
Shenzhen Institute for Quantum Science and Engineering（深圳量子科学与工程研究院）；Southern University of Science and Technology（南方科技大学）；International Quantum Academy（国际量子学院）；City University of Hong Kong（香港城市大学）
Pre- and post-selected (PPS) measurement, especially the weak PPS measurement, is a useful protocol for amplifying small physical parameters. However, it is difficult to retain both the attainable highest measurement sensitivity and precision with the increase of the parameter to be measured. Here, a modulated PPS measurement scheme based on coupling-strength-dependent modulation is presented with the highest sensitivity and precision retained for an arbitrary coupling strength. This idea is demonstrated by comparing the modulated PPS measurement scheme with standard PPS measurementv scheme, r…
The Decodoku project seeks to let users get hands-on with cutting-edge quantum research through a set of simple puzzle games. The design of these games is explicitly based on the problem of decoding qudit variants of surface codes. This problem is presented such that it can be tackled by players with no prior knowledge of quantum information theory, or any other high-level physics or mathematics. Methods devised by the players to solve the puzzles can then directly be incorporated into decoding algorithms for quantum computation. In this paper we give a brief overview of the novel decoding met…
Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric Rényi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric Rényi relative entropy for the interval $α\in(0,1) $ of the Rényi parameter $α$. In …
