Related papers: Structural Features of Sequential Weak Measurement…
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…
We present a full-sky derivation of weak lensing observables in the Post-Friedmann (PF) formalism. Weak lensing has the characteristic of mixing small scales and large scales since it is affected by inhomogeneities integrated along the…
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
Mixed states can exhibit two distinct kinds of symmetries, either on the level of the individual states (strong symmetry), or only on the level of the ensemble (weak symmetry). Strong symmetries can be spontaneously broken down to weak…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics. Specifically, we consider a forward'' weak measurement from a preselected state $\ket{\psi}$ to a post-selected state…
We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner…
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…
The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being…
A weakly consecutive sequence (WCS) is a permutation $\sigma$ of $\{1, \ldots, k\}$ such that if an integer $d$ divides $\sigma(i)$, then $d$ also divides $\sigma(i \pm d)$ insofar as these are defined. The structure of weakly consecutive…
Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
In this article, we study quantum coherence of bipartite state from the perspective of weak measurement, which generalizes the notion of coherence relative to measurement. The is being illustrated by computing coherence for the well-known…
Geometrical dephasing is distinct from dynamical dephasing in that it depends on the trajectory traversed, hence it reverses its sign upon flipping the direction in which the path is traced. Here we study sequences of generalized (weak)…
Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of…
Weak measurement [1,19] combined with quantum delayed-choice experiment that use quantum beam splitter instead of the beam splitter give rise to a surprising amplification effect, i.e., counterintuitive negative amplification effect. We…
Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur…
We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain. The asymptotic…