Y. Aharonov, L. Vaidman
A recent result about measurability of a quantum state of a single quantum system is generalized to the case of a single pre- and post-selected quantum system described by a two-state vector. The protection required for such measurement is achieved by coupling the quantum system to a pre- and post-selected protected device yielding a nonhermitian effective Hamiltonian.
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We generalize protective measurement for protective joint measurement of several observables. The merit of joint protective measurement is the determination of the eigenstates of an unknown Hamiltonian rather than the determination of features of an unknown quantum state. As an example, we precisely determine the two eigenstates of an unknown Hamiltonian by a single joint protective measurement of the three Pauli matrices on a qubit state.
Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider ``protective measurements'' [Phys. Lett. A 178, 38 (1993)] which we have recently introduced. We show that the measurements discussed by Alter and Yamamoto ``are not'' the protective measurements we proposed. Therefore, their results are irrelevant to the nature of protective measurements.
My view on the meaning of the quantum wave function and its connection to protective measurements is described. The wave function and only the wave function is the ontology of the quantum theory. Protective measurements support this view although they do not provide a decisive proof. A brief review of the discovery and the criticism of protective measurements is presented. Protective measurements with postselection are discussed.
Making measurements on single quantum systems is considered difficult, almost impossible if the state is a-priori unknown. Protective measurements suggest a possibility to measure single quantum systems and gain some new information in the process. Protective measurement is described, both in the original and generalized form. The degree to which the system and the apparatus remain entangled in a protective measurement, is assessed. A possible experimental test of protective measurements is discussed.
It has been debated whether protective measurement implies the reality of the wave function. In this paper, I present a new analysis of the relationship between protective measurements and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy's theorem in terms of protective measurements. Third, I analyze two suggested $ψ$-epistemic models of a protective measurement. It is shown that although these models can explain the appearance of expectation values of observables in a sing…
Performance advantage of protective quantum measurements
该研究对比保护性量子测量与标准投影测量的性能，以测量期望值不确定度量化性能，推导两类测量的相对性能表达式，证实保护性测量具备显著性能优势。
A review of protective measurements. Protective measurement is a method for measuring an expectation value of an observable on a single quantum system. The quantum state of the system can be protected by a potential, when the state is a nondegenerate energy eigenstate with a known gap to neighboring states, or via Zeno effect by frequent projection measurements.
A new type of procedures, called protective measurements, has been proposed by Aharonov, Anandan and Vaidman. These authors argue that a protective measurement allows the determination of arbitrary observables of a single quantum system and claim that this favors a realistic interpretation of the quantum state. This paper proves that only observables that commute with the system's Hamiltonian can be measured protectively. It is argued that this restriction saves the coherence of alternative interpretations.
A distinguishing feature of protective measurement is the possibility of obtaining information about expectation values while making the disturbance of the initial state arbitrarily small. Quantifying this state disturbance is of paramount importance. Here we derive exact and perturbative expressions for the state disturbance and the faithfulness of the measurement outcome in a model describing a spin-1/2 particle protectively measured by an inhomogeneous magnetic field. We determine constraints on the experimentally required field strengths from bounds imposed on the allowable state disturban…
We examine the entanglement and state disturbance arising in a protective measurement and argue that these inescapable effects doom the claim that protective measurement establishes the reality of the wave function. An additional challenge to this claim results from the exponential number of protective measurements required to reconstruct multi-qubit states. We suggest that the failure of protective measurement to settle the question of the meaning of the wave function is entirely expected, for protective measurement is but an application of the standard quantum formalism, and none of the hard…
Protective measurements illustrate how Yakir Aharonov's fundamental insights into quantum theory yield new experimental paradigms that allow us to test quantum mechanics in ways that were not possible before. As for quantum theory itself, protective measurements demonstrate that a quantum state describes a single system, not only an ensemble of systems, and reveal a rich ontology in the quantum state of a single system. We discuss in what sense protective measurements anticipate the theorem of Pusey, Barrett, and Rudolph (PBR), stating that, if quantum predictions are correct, then two distinc…
We investigate the disturbance of the state of a quantum system in a protective measurement for finite measurement times and different choices of the time-dependent system-apparatus coupling function. The ability to minimize this state disturbance is essential to protective measurement. We show that for a coupling strength that remains constant during the measurement interaction of duration $T$, the state disturbance scales as $T^{-2}$, while a simple smoothing of the coupling function significantly improves the scaling behavior to $T^{-6}$. We also prove that the shift of the apparatus pointe…
Classical ergodicity retains its meaning in the quantum realm when the employed measurement is protective. This unique measuring technique is reexamined in the case of post-selection, giving rise to novel insights studied in the Heisenberg representation. Quantum statistical mechanics is then briefly described in terms of two-state density operators.
We present a detailed description of the experiment realising for the first time a protective measurement, a novel measurement protocol which combines weak interactions with a ``protection mechanism'' preserving the measured state coherence during the whole measurement process. Furthermore, protective measurement allows finding the expectation value of an observable, i.e. an inherently statistical quantity, by measuring a single particle, without the need of any statistics. This peculiar property, in sharp contrast with the framework of traditional (projective) quantum measurement, might const…
This paper presents a proof-of-principle scheme for the protective measurement of a single photon. In this scheme, the photon is looped arbitrarily many times through an optical stage that implements a weak measurement of a polarization observable followed by a strong measurement protecting the state. The ability of this scheme to realize a large number of such interaction-protection steps means that the uncertainty in the measurement result can be drastically reduced while maintaining a sufficient probability for the photon to survive the measurement.
"Protective measurement" refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a "protecting" operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconst…
Protective measurements of photon polarization using a temporal pointer
该研究利用光子到达时间作测量指针，通过光学环实现1-9个可控的保护测量阶段，在无需初始态信息的情况下测得光子偏振期望值，证明保护性测量可提供非先验的真实信息增益。
Recently proposed idea of "protective" measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed and their relevance to the proposal assessed. Several constraints on measuring apparatus required by "protective" measurements are discussed, with emphasis on how they may restrict their experimental feasibility. Though "protective" measurements result in an unchanged system state and a shift of the pointer proportional to the expectation value of the measured observable in the system state, the actual reading of the pointer position gives …
Protective measurements which were defined by Aharonov and Vaidman in 1993 played an important role in the discussion about the interpretation of quantum mechanics. In 1999, following an early work by Englert et al., Aharonov et al. wrote an article in which they showed that protective measurements can be used to demonstrate the `surrealism' of Bohmian mechanics. Bohmian mechanics also known as pilot-wave interpretation is certainly the best-known hidden variable interpretation of quantum mechanics. It played a fundamental role in the discovery by Bell of his famous non locality theorem. There…
In the above paper [1], it is claimed that Bohm's mechanics can be challenged by a simple gedanken experiment involving a protecting measurement. Here we show that this gedanken experiment can be justified without problem and without contradicting the axiom attributing a physical meaning to the Bohmian trajectorie
We study protective quantum measurements in the presence of an environment and decoherence. We consider the model of a protectively measured qubit that also interacts with a spin environment during the measurement. We investigate how the coupling to the environment affects the two characteristic properties of a protective measurement, namely, (i) the ability to leave the state of the system approximately unchanged and (ii) the transfer of information about expectation values to the apparatus pointer. We find that even when the interaction with the environment is weak enough not to lead to appr…
Here we show that, in principle it is possible to clone (measure) a single arbitrary unknown quantum state of a spin-$\frac{1}{2}$ particle (an electron) with arbitrary precision and with success probability tending to one, using protective measurement. We first transfer the information from spin to spatial degree of freedom (d.o.f) of system electron, then trap it in a double well potential, and finally measure it protectively using a probe electron (which donot get entangled with system electron, but still extracts expectation value of an observable from a single quantum system (system elect…
Active polarization stabilization of fields in an optical fiber for protective measurements
通过在双折射光纤中主动稳定偏振，利用光子计数实现更高信号和更低背景的Zeno保护测量
We study the protective measurement of a qubit by a second qubit acting as a probe. Consideration of this model is motivated by the possibility of its experimental implementation in multiqubit systems such as trapped ions. In our scheme, information about the expectation value of an arbitrary observable of the system qubit is encoded in the rotation of the state of the probe qubit. We describe the structure of the Hamiltonian that gives rise to this measurement and analyze the resulting dynamics under a variety of realistic conditions, such as noninfinitesimal measurement strengths, repeated m…
Conventionally, unknown quantum states are characterized using quantum-state tomography based on strong or weak measurements carried out on an ensemble of identically prepared systems. By contrast, the use of protective measurements offers the possibility of determining quantum states from a series of weak, long measurements performed on a single system. Because the fidelity of a protectively measured quantum state is determined by the amount of state disturbance incurred during each protective measurement, it is crucial that the initial quantum state of the system is disturbed as little as po…
Protective measurements yield properties of the quantum state of a single quantum system without affecting the quantum state. A protective measurement involves adiabatic coupling to the measuring device together with a procedure to protect the state from changing. For nondegenerate energy eigenstates the protection is provided by the system itself. In this case it is actually possible to measure the Schrödinger wave via measurements on a single system. This fact provides an argument in favor of associating physical reality with a quantum state of a single system, challenging the usual ensemble…
In this article we propose an alternate model for the so called {\it protective measurements}, more appropriately {\it adiabatic measurements} of a spin 1/2 system where the {\it apparatus} is also a quantum system with a {\em finite dimensional Hilbert space}. This circumvents several technical as well as conceptual issues that arise when dealing with an infinite dimensional Hilbert space as in the analysis of conventional Stern-Gerlach experiment. Here also it is demonstrated that the response of the detector is continuous and it {\it directly} measures {\em expectation values without alteri…
Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of this concept on the debate between the epistemological and ontological viewpoints. The theoretical merits of the empty wave in avoiding the wavefunction collapse hypothesis, and in supplying conceptual precision in the application of quantum mechanics, are emphasized. Particular reference is made to path detection in interferometry and it is shown…
The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality of the quantum state in the framework. For example, the Pusey-Barrett-Rudolph theorem is based on an additional preparation independence assumption. In this paper, we give a new proof of psi-ontology in terms of protective measurements in the ontological model framework. The proof does not rely on auxiliary assumptions, and also applies to …
Simulating single-photon experiments with a quantum computer
本研究使用量子计算机模拟实验室中光子的行为，对比保护性与非保护性测量下的模拟结果与理论预测，揭示了量子计算机在模拟实际物理系统时的效率表现。
The dynamics of any quantum system is unavoidably influenced by the external environment. Thus, the observation of a quantum system (probe) can allow the measure of the environmental features. Here, to spectrally resolve a noise field coupled to the quantum probe, we employ dissipative manipulations of the probe, leading to so-called Stochastic Quantum Zeno (SQZ) phenomena. A quantum system coupled to a stochastic noise field and subject to a sequence of protective Zeno measurements slowly decays from its initial state with a survival probability that depends both on the measurement frequency …
``Weak'', ``protective'', and ``delayed observation'' measurements are analyzed in the framework of the Bohm interpretation of quantum theory. It is argued that the above varieties of measurements manifest some difficulties of the Bohm interpretation since they show that Bohmian trajectories behave not as we would expect from a classical type model.
In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations which he dramatized using a parable about a seer who sets an impossible prediction task to his daughter's suitors. We revisit this example here, using it as an entree to three central concepts in quantum foundations: contextuality, Bell-nonlocality, and complementarity. Specifically, we show that Specker's parable offers a narrative thread that weaves together a large number of results, including: the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum…
We suggest scattering experiments which implement the concept of ``protective measurements'' allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering experiments require massive, slow, projectiles with kinetic energies lower than the first excitation of the system in question. The results of such experiments can have a (probabilistic) distribution (as is the case when the Born approximation for the scattering is valid) or be deterministic (in a semi-classical limit).
Measurements are crucial in quantum mechanics, in fundamental research as well as in applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polar…
Conventional strategies of quantum metrology are built upon POVMs, thereby possessing several general features, including the demolition of the state to be measured, the need of performing a number of measurements, and the degradation of performance under decoherence and dissipation. Here, we propose an innovative measurement scheme, called dissipative adiabatic measurements (DAMs), based on which, we further develop an approach to estimation of parameters characterizing dissipative processes. Unlike a POVM, whose outcome is one of the eigenvalues of an observable, a DAM yields the expectation…
Protective measurement, which was proposed as a method of observing the wavefunction of a single system, is extended to the observation of the density matrix of a single system. d'Espagnat's definition of `proper mixture' is shown to be improper because it does not allow for appropriate fluctuations. His claim that there could be different mixtures corresponding to the same density matrix is critically examined. These results provide a new meaning to the density matrix, which gives it the same ontological status as the wavefunction describing a pure state. This also enables quantum entropy to …
It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of these vectors are discussed, as well as some connexions with the quantum-mechanical formalism.
Quantum mechanics, one of the keystones of modern physics, exhibits several peculiar properties, differentiating it from classical mechanics. One of the most intriguing is that variables might not have definite values. A complete quantum description provides only probabilities for obtaining various eigenvalues of a quantum variable. These and corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property of an ensemble of quantum systems. In contrast to this paradigm, we demonstrate a unique method allowing to measure the expecta…
The notion of collapse is discussed and refined within the Two-State-Vector Formalism (TSVF). We show how a definite result of a measurement can be fully determined when considering specific forward and backward-evolving quantum states. Moreover, we show how macroscopic time-reversibility is attained, at the level of a single branch of the wavefunction, when several conditions regarding the final state and dynamics are met, a property for which we coin the term "classical robustness under time-reversal". These entail a renewed perspective on the measurement problem, the Born rule and the many-…
Deterministic nuclear spin squeezing and squeezing by continuous measurement using vector and tensor light shifts
研究矢量和张量光移对大自旋原子的联合影响，通过测量率Γ和耦合比ε确定量子非破坏测量压缩和确定性压缩的条件，应用于具有纯核自旋的原子以实现低退相干的自旋方差压缩。
Evolution of a physical quantum state vector is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. In previous literature, it was concluded that a relativistically satisfactory version of the collapse postulate is in contradiction with physical measurements of a non-local state history. Here it is shown that such measurements are excluded when reduction is formulated as a physical process and the measurement devices are included as part of the state vector.
The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of "direct measurement" was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While this method has been used for measuring polarization states, its real potential lies in the measurement of states with a large dimensionality. Here we show the practical direct measurement of a high-dimensional state vector in the discrete basis of orbital-angular momentum. Through weak measurements of orbital-angular momentum and strong measurements of ang…
Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused…
We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making singleshot polarization-dependent measurements, as well as for providing a means of preparing samples with position-de…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of the state vector at measurements. Probabilities are computed by summing the squares of amplitudes over alternatives which could have been measured but weren't. Measurements are limited by uncertainty principles and by other restrictions arising from the principles of quantum mechanics. This essay examines the extent to which those features of the quantum mec…
We use differential Ramsey interferometry of ultracold atoms to characterize the vector light shift (VLS) from a far-off resonance optical dipole trap at $λ= 1064\,\mathrm{nm}$. The VLS manifests as a `fictitious' magnetic field, which we perceive as a change in the Larmor frequency of two spinor condensates exposed to different intensities of elliptically polarized light. We use our measurement scheme to diagnose the light-induced magnetic field and suppress it to $2.1(8)\times10^{-4}$ of its maximum value, by making the trapping light linearly polarized with a quarter-wave plate in each beam…
In this article we propose a dynamic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure quantum system is given by the Schrödinger equation with a time-independent Hamiltonian and the other states that the knowledge about the quantum state is provided from projective measurements, also called intensity measurements. The problem of quantum state reconstruction is connected with the notion known as phase retrieval -- recovering a complex vector from mo…
The information-theoretic formulation of quantum measurement uncertainty relations (MURs), based on the notion of relative entropy between measurement probabilities, is extended to the set of all the spin components for a generic spin s. For an approximate measurement of a spin vector, which gives approximate joint measurements of the spin components, we define the device information loss as the maximum loss of information per observable occurring in approximating the ideal incompatible components with the joint measurement at hand. By optimizing on the measuring device, we define the notion o…
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