Related papers: What is the value of an observable between pre- an…
The physical meaning of weak values and measurements can be completely understood with Born rule and the general probability theory. It is known that the weak value of an observable $\hat A$ with post-selection $\langle F|$ may be out of…
The variance of an observable in a pre-selected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and post-selected…
It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems…
In a weak measurement the real and imaginary parts of a weak value participate in the shifts of the complementary variables of a pointer. While the real part represents the value of an observable in the limit of zero measurement strength,…
Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
Halls exact variance decomposition [Phys. Rev. A 64, 052103 (2001)] splits the quantum variance of an observable into the ensemble variance of an optimal position based estimate and a residual nonclassical inaccuracy. We evaluate this…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of pre-and-post-selection (PPS), it is possible to assign definite values to observables in a new and surprising way. Physical reasons are presented for restrictions…
The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model…
Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the…
A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it,…
After an elementary derivation of Bell's inequality, several forms of expectation functions for two-valued observables are discussed. Special emphasis is given to hypothetical stronger-than quantum expectation functions which give rise to a…
The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…
Svensson [Found. Phys. 45, 1645 (2015)] argued that the concept of the weak value of an observable of a pre- and post-selected quantum system cannot be applied when the expectation value of the observable in the initial state vanishes.…
Controllability and observability are important properties of a distributed paramater systems.The equivalence between the notion of exact observability and exact controllability holds in general. In this work, we define a new notion of…
A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
The traditional optical concept for the object does not provide an experimental feasibility to speak for itself, due to the fact that no measuring instrument catches up with the fluctuation of light fields. Using the theory of coherence, we…
The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or…