Lars M. Johansen
Hall's recent derivation of an exact uncertainty relation [Phys. Rev. A64, 052103 (2001)] is revisited. It is found that the Bayes estimator of an observable between pre- and postselection equals the real part of the weak value. The quadratic loss function equals the expectation of the squared imaginary part of the weak value.
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We propose a new protocol for the weak measurement of any observable with remote pre and postselections. We show that if two parties share a pure entangled state, then by using local operations and classical communication they can preselect and postselect at distant locations leading to the weak value of an observable as a shift in the pointer of the apparatus at one location in the process of the weak measurement. This can be achieved with either sharing of a pure maximally or non-maximally entangled state. We generalize the protocol for realizing the weak value of any observable with remote …
No-go result for quantum postselection measurements of rank-m degenerate subspace
本文证明了当联合系统-设备可观测量具有秩-m简并性时，后选择测量无法改变其条件期望值，并据此表明量子测量的误差-扰动不确定性在后选择下保持不变。
Pre-Asymptotic Trainability in Photonic Variational Circuits under Postselection
研究光子变分电路中后选择对梯度集中度的影响，发现碰撞自由和允许成簇演化下梯度方差呈多项式衰减，而双轨后选择在较大系统规模下导致指数集中，揭示了被动线性光学动力学、后选择几何和任务可观测量的相互作用。
Postselection in lattice bosons undergoing continuous measurements
本文研究连续局域测量下晶格玻色子的后选择问题，提出将测量记录压缩为一两个数再后选择的协议，并解析和数值证明其能以低开销恢复量子轨迹关联函数，且所需信息可从非条件动力学和测量记录中独立获取。
We propose a new model of quantum computation which aims to speed up quantum algorithms assisted by the weak value amplification and ancillay quantum register with the pre- and postelection. Within this model, we show that a quantum computer can solve a data base search of N entries in one step with probability close to one for large N, provided the post-selection on the ancillary quantum register is successful. In this model, to search a data base of N entries, the number of qubits grows from n to 2n, but there is a huge reduction in time complexity. Physically, this can be understood as the …
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define and, if not sufficiently accurate, they provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully sepa…
In the weak measurement (WM) scenario involving weak interaction and postselection by projective measurement, the empirical significance of weak values is manifested in terms of shifts in the measurement pointer's mean position and mean momentum. In this context, a general quantitative treatment is presented in this paper by taking into account the hitherto unexplored effect of correlations among the pointer degrees of freedom which pertain to an arbitrary multidimensional preselected pointer state. This leads to an extension of the earlier results, showing that, for complex weak values, the c…
While the novel applications of weak values have recently attracted wide attention, weak measurement, the usual way to extract weak values, suffers from risky approximations and severe quantum noises. In this paper, we show that the weak-value information can be obtained exactly in strong measurement with postselections, via measuring the coupling-deformed pointer observables, i.e., the observables selected according to the coupling strength. With this approach, we keep all the advantages claimed by weak-measurement schemes and at the same time solve some widely criticized problems thereof, su…
The application of postselection to a weak quantum measurement leads to the phenomenon of weak values. Expressed in units of the measurement strength, the displacement of a quantum coherent measuring device is ordinarily bounded by the eigenspectrum of the measured observable. Postselection can enable an interference effect that moves the average displacement far outside this range, bringing practical benefits in certain situations. Employing the Fisher information metric, we argue that the amplified displacement offers no fundamental metrological advantage, due to the necessarily reduced prob…
A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To obtain the weak value of a variable $A$ one performs weak measurements twice, with different initial states of the "meter" field. This seems to be a drawback, but as a compensation we get for free the weak value of a complementary variable $B$. The scheme is tunable and versatile: one has access to a continuous set of possible weak measurements of pair of o…
An imprecise measurement of a dynamical variable (such as a spin component) does not, in general, give the value of another dynamical variable (such as a spin component along a slightly different direction). The result of the measurement cannot be interpreted as the value of any observable that has a classical analogue.
Dimension-independent weak value estimation via controlled SWAP operations
提出一种基于受控SWAP操作的确定性且维度无关的弱值估计方案，用于估计任意可观测量的弱值，并揭示了双时态与正部分转置双量子态之间的联系。
Quantum weak measurements with states both pre- and postselected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two very simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The postselection criteria are chosen as follows: at the final time, the "atom" remains in its initial excited state for the first example and the particle remains behind the barrier for …
In recent work (Nii et al., arXiv:1603.06291; Iinuma et al., Phys. Rev. A 93, 032104 (2016)(arXiv:1510.03958)) we have studied the relation between experimental outcomes and the physical properties represented by Hilbert space operators of a quantum system. We find that the values of physical properties are determined by the combination of initial and final conditions, which means that eigenstates and eigenvalues should not be misinterpreted as an exclusive set of possible realities. Here, we discuss the practical implications of these results and point out the importance of quantitative relat…
Anomalous Weak Pointer Shifts as Postselected Interference among Coarse-Grained Histories
本研究用相空间路径积分语言重新表述反常弱指针偏移效应，证明其源于有限粗粒化历史间的后选择相干干涉，并探讨了该图景对守恒律问题的意义。
Using the Naimark dilation theory we investigate the question under what conditions an observable which is a coarse graining of another observable is a function of it. To this end, conditions for the separability and for the Boolean structure of an observable are given.
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective measurements. However, a classical model has been recently put forward that can reproduce peculiar expectation values, reminiscent of weak values. This led the authors of that work to claim that weak values have an entirely classical explanation. Here we discuss what is quantum about weak values with the help of a simple model based on basic quantum mechanics. We fir…
Relativity theory severely restricts the ability to perform nonlocal measurements in quantum mechanics. Studying such nonlocal schemes may thus reveal insights regarding the relations between these two fundamental theories. Therefore, for the last several decades, nonlocal measurements have stimulated considerable interest. However, the experimental implementation of nonlocal measurements imposes profound restrictions due to the fact that the interaction Hamiltonian cannot contain, in general, nonlocal observables such as the product of local observables belonging to different particles at spa…
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a subjective lack of information regarding the physical reality of the system. In the present paper, I explore how the operator formalism accommodates the vast number of possible states and measurements by characterizing its essential function as a description of causality relations between initial conditions and subsequent observations. It is shown that any complete…
What is electric charge?: Charge as a local observable in relativistic quantum field theory
本文针对相对论量子场论中电荷未被明确定义为局域可观测量的问题，基于 $C^{*}$-代数框架，提出范围局域电荷 $Q_{\boldsymbol{\nu}}(P)$ 的概念，回应电荷算符的局域化问题。
Precise definitions of "weak [quantum] measurements" and "weak value" [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional examples are given showing that weak values of an observable are not unique, and in fact arbitrary weak values can be obtained by appropriate weak measurements. This implies that a "weak value" of an observable A, *by itself*, can furnish no unambiguous information about A; any information in a weak value is inextricably connected with the particular measureme…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including but not reducible to what other measurements are made "together" with the given one. We propose in this paper that the quantum observables generating these random variables be labeled contextually as well, making the sets of the observables in different contexts disjoint. A quantum observable is defined as a pair consisting of the observable's label and a sel…
This is a comment on J. A. Barrett's article ``The Preferred-Basis Problem and the Quantum Mechanics of Everything'' in Brit. J. Phil. Sci. 56 (2005), which concerns theories postulating that certain quantum observables have determinate values, corresponding to additional (often called ``hidden'') variables. I point out that it is far from clear, for most observables, what such a postulate is supposed to mean, unless the postulated additional variable is related to a clear ontology in space-time, such as particle world lines, string world sheets, or fields.
The role of measurement induced disturbance in weak measurements is of central importance for the interpretation of the weak value. Uncontrolled disturbance can interfere with the postselection process and make the weak value dependent on the details of the measurement process. Here we develop the concept of a generalized weak measurement for classical and quantum mechanics. The two cases appear remarkably similar, but we point out some important differences. A priori it is not clear what the correct notion of disturbance should be in the context of weak measurements. We consider three differe…
Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what will happen if physical observables are allowed to take complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using loc…
Super-phenomena in arbitrary quantum observables
该研究将超振荡推广到任意量子算符的弱值场景，提出算符弱值超本征值界限时出现超行为，通过总角动量和能量示例验证，还提供数值证据支持相关效应。
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three Box paradox and Hardy s paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in c…
What is special about the Kirkwood-Dirac distributions? Only they produce natural conditional expectations
本文证明，在所有与可观测量 $\hat A$ 和 $\hat B$ 的 Born 概率兼容的准概率表示中，只有 Kirkwood-Dirac 表示能提供与量子条件期望一致的条件期望概念。
In a recent paper [quant-ph/9910066], Arens and Varadarajan gave a characterization of what they call EPR-states on a bipartite composite quantum system. By definition, such states imply perfect correlation between suitable pairs of observables in the two subsystems, and the task is to determine all such correlated pairs for a given state. In this note the argument is shortened and simplified, and at the same time extended to observables in general von Neumann algebras, which naturally arise in quantum field theory.
In a weak measurement, the average output $\langle o\rangle$ of a probe that measures an observable $\hat{A}$ of a quantum system undergoing both a preparation in a state $ρ_i$ and a postselection in a state $E_\mathrm{f}$ is, to a good approximation, a function of the weak value $A_w=\mathrm{Tr} [E_f \hat{A} ρ_i]/\mathrm{Tr}[E_fρ_i]$, a complex number. For a fixed coupling $λ$, when the overlap $\mathrm{Tr}[E_fρ_i]$ is very small, $A_w$ diverges, but $\langle o\rangle$ stays finite, often tending to zero for symmetry reasons. This paper answers the questions: what is the weak value that maxim…
This paper defines what constitutes the Observed World in the Quantum Mechanical framework, based strictly on what is actually observed beyond doubt, instead of building observables on what is inferred from actual observations. Such principle narrows down considerably what can be considered as being part of the Observed World. On the other hand, we argue that some information - that is in general assumed as granted - should actually be considered as being part of the Observed World. We discuss the implications of such assertion, in the way we perceive time evolution, information growth and cau…
What do position and time mean in the quantum wavefunction?
本研究针对量子波函数中位置与时间的数学地位等教学问题，构建统一教学框架，厘清相关概念并展示存在正则自伴时间可观测量的边界案例，为量子力学教学提供支持。
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