An entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg
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.
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…
An alternate model for protective measurements of two-level systems
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…
Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimation. Since many quantities can be converted to phase signal, it is thus interesting and important to consider measuring ultra-small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification based ultra-small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of…
Measuring measurement--disturbance relationships with weak values
使用测量精度ε和扰动（测量反作用）η的形式定义，Ozawa [Phys. Rev. A 67，042105（2003）]已经表明海森堡声称的这些量之间的关系一般是错误的。在这里，我们表明，小泽介绍的数量可以通过实验确定，使用没有先验知识的测量调查-这两个数量对应的根均方差由弱值概率分布。我们提出了一个简单的三量子比特实验，这将说明海森堡的测量-扰动关系的失败，和小泽提出的替代关系的有效性。
State of a $d$-dimensional quantum system can only be inferred by performing an informationally complete measurement with $m\geqslant d^2$ outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here we show that a single informationally incomplete measuring apparatus is still able to provide all the information about the quantum system if applied several times in a row. We derive a necessary and sufficient condition for such a measuring apparatus and give illustrative examples for qubits, qutrits, general $d$-level systems, and composite systems of $n$ q…
Work is an observable quantity associated with a process, however there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von-Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality an…
We have implemented the six series of three commuting measurement of the Mermin-Peres magic square on an online, five qubit, quantum computer. The magic square tests if the measurements of the system can be described by physical realism (in the EPR sense) and simultaneously are non-contextual. We find that our measurement results violate any realistic and non-contextual model by almost 28 standard deviations. We also find that although the quantum computer we used for the measurements leaves much to be desired in producing accurate and reproducible results, the simplicity, the ease of re-runni…
