Related papers: Optimal weak measurements: Mixed States
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in…
It is known that protocols based on weak measurements can be used to steer quantum systems into pre-designated pure states. Here we show that weak-measurement-based steering protocols can be harnessed for on-demand engineering of…
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 $\rho_i$ and a postselection in a state $E_\mathrm{f}$ is, to a good…
Historically, weak values have been associated with weak measurements performed on quantum systems. Over the past two decades, a series of works have shown that weak values can be determined via measurements of arbitrary strength. One such…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
We discuss two questions related to the concept of weak values as seen from the standard quantum-mechanics point of view. In the first part of the paper, we describe a scenario where unphysical results similar to those encountered in the…
Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and non-distillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely…
In this paper we present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles.…
We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and nonnegative in…
A weak measurement approach is proposed to entangle and squeeze atoms. We show that even for very small coupling strength between light and atoms, one can achieve large squeezing unattainable with normal measurement-based squeezing.…
Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements…
The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum…
In a recent Letter (Phys. Rev. Lett. 109, 040401 (2012)), G. Puentes, N. Hermosa and J. P. Torres report a scheme for extracting higher-order weak values by using orbital-angular momentum states as pointer states. They claim that such weak…
We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are…
Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the…
A mathematical extension of the weak value formalism to the simultaneous measurement of multiple parameters is presented in the context of an optical focused vector beam scatterometry experiment. In this example, preselection and…
We examine weak measurements of arbitrary observables where the object is prepared in a mixed state and on which measurements with imperfect detectors are made. The weak value of an observable can be expressed as a conditional expectation…