Related papers: Weak measurements are universal
The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures.…
The Cram\'er-Wold device characterises weak convergence of probability measures on $\mathbb{R}^d$ through convergence of all one-dimensional projected laws. We prove that, if the target projected laws are moment-determinate for…
We propose a new protocol for the weak measurement of any observable with remote pre and postselections. We show that if two parties share a pure entangled state, then by using local operations and classical communication they can preselect…
We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call epsilon-measures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate…
We show that almost any one-dimensional projection of a suitably scaled random walk on a hypercube, inscribed in a hypersphere, converges weakly to an Ornstein-Uhlenbeck process as the dimension of the sphere tends to infinity. We also…
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…
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…
Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with…
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…
Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the…
Complete measurement of a quantum observable (POVM) is a measurement of the maximally refined version of the POVM. Complete measurements give information on multiplicities of measurement outcomes and can be viewed as state preparation…
The readings of a highly inaccurate "weak" quantum meter, employed to determine the value of a dichotomous variable $S$ without destroying the interference between the alternatives,may take arbitrary values. We show that the expected values…
We expand our effective framework for weak convergence of measures on the real line by showing that effective convergence in the Prokhorov metric is equivalent to effective weak convergence. In addition, we establish a framework for the…
Recent empirical work in the field of 'weak measurements' has yielded novel ways of more directly accessing and exploring the quantum wavefunction. Measuring either position or momentum for a photon in a 'weak' manner yields a wide range of…
In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured…
The apparent nonunitary evolution in the black hole information paradox and recent work on describing wavefunction collapse via nonunitary nonlinear stochastic operators has motivated us to analyze whether mixed states can be distinguished…
Based on a weak convergence argument, we provide a necessary and sufficient condition that guarantees that a nonnegative local martingale is indeed a martingale. Typically, conditions of this sort are expressed in terms of integrability…
When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement back-action. We introduce, and push to its theoretical and…
For a quantum system undergoing a unitary process work is commonly defined based on the Two Projective Measurement (TPM) protocol which measures the energies of the system before and after the process. However, it is well known that…
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary…