Related papers: Optimal weak value measurements: Pure states
The problem addressed is to design a detector which is maximally sensitive to specific quantum states. Here we concentrate on quantum state detection using the worst-case a posteriori probability of detection as the design criterion. This…
Knowing about optimal quantum measurements is important for many applications in quantum information and quantum communication. However, deriving optimal quantum measurements is often difficult. We present a collection of results for…
The aim of this work is to estimate a quadratic functional of a unknown Wigner function from noisy tomographic data. The Wigner function can be seen as the representation of the quantum state of a light beam. The estimation of a quadratic…
Weak measurements with mixed probe states were investigated in the presence of noise in the probe system. We show that the completely mixed state can be used as a probe state for weak measurements of imaginary weak values. The completely…
Consider a photon that has just emerged from a linear polarizing filter. If the photon is then subjected to an orthogonal polarization measurement-e.g., horizontal vs vertical-the photon's preparation cannot be fully expressed in the…
We enumerate the micro-states in Higgs theories, addressing (i) the number of vacuum states and (ii) the appropriate measure in the quantum path integral. To address (i) we explicitly construct the set of ground state wave-functionals in…
Practical quantum state tomography is usually performed by carrying out repeated measurements on many copies of a given state. The accuracy of the reconstruction depends strongly on the dimensionality of the system and the number of copies…
We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.
Positive operator valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2 J+1) covariant constraint. This…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
Given $n$ linearly independent pure states and their prior probabilities, we study the problem of optimum unambiguous discrimination of these states. We derive the properties of the optimum solution and the equations that must be satisfied…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal…
The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by…
It is shown that the attempt to extend the notion of ideal measurement to quantum field theory leads to a conflict with locality, because (for most observables) the state vector reduction associated with an ideal measurement acts to…
We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric downconversion. The states are characterised using measures of…
We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert…
The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of \emph{weak measure solutions}, with and without angular cutoff on the…