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Weak measurement is a novel technique for parameter estimation with higher precision. In this paper we develop a general theory for the parameter estimation based on weak measurement technique with arbitrary postselection. The previous weak…

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…

The notion of weak measurement in quantum mechanics has gained a significant and wide interest in realizing apparently counterintuitive quantum effects. In recent times, several theoretical and experimental works have been reported for…

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…

All compositions of a mixed-state density operator are equivalent for the prediction of the probabilities of future outcomes of measurements. For retrodiction, however, this is not the case. The retrodictive formalism of quantum mechanics…

Many quantum paradoxes based on a realistic view of weak values were discussed in the last decades. They lead to astonishing conclusions such as the measurement of a spin component of a spin-1/2 particle resulting in $100\hbar$, the…

In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since…

An upper bound between the information gain and state reversibility of weak measurement was first developed by Y. K. Cheong and S. W. Lee [Phys. Rev. Lett. 109, 150402 (2012)]. Their results are valid for arbitrary d-level quantum systems.…

LANL Memorandum of potentially broad interest. A direct comparison is performed between transport coefficients for weakly coupled plasmas obtained with different formalisms to demonstrate that these formalisms give identical predictions.…

Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify…

In this presentation, I argue that weak measurements empirically support the notion of quantum superpositions as statistical alternatives. In short, weak measurements show that Schroedinger's cat is already dead or alive before the…

There is suggested a version of the experiment with a correlated pair of particles in the entangled state. The experiment demonstrates that, in the case of weak and/or non-demolition measurements of one of the particles, it is possible to…

The models we use, habitually, to describe quantum nonlinear optical processes have been remarkably successful yet, with few exceptions, they each contain a mathematical flaw. We present this flaw, show how it can be fixed and, in the…

As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local-hidden variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a…

One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…

We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative…

The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…

In this paper we study Hardy and Poincar\'e inequalities and their weak versions for quadratic forms satisfying the first Beurling-Deny criterion. We employ these inequalities to establish a criticality theory for such forms.

In this work we establish a link between two apparently unrelated subjects: polarization effects in optical fibers and devices, and the quantum theory of weak measurements. We show that the abstract concept of weak measurements followed by…

We investigate a specific set of two-loop self-energy corrections involving squared decay rates and point out that their interpretation is highly problematic. The corrections cannot be interpreted as radiative energy shifts in the usual…