Related papers: The Helstrom Bound
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
Under some physical considerations, we present a universal formulation to study the possibility of localizing a quantum object in a given region without disturbing its unknown internal state. When the interaction between the object and…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in…
We study minimum-error identification of an unknown single-bit Boolean function given black-box (oracle) access with one allowed query. Rather than stopping at an abstract optimal measurement, we give a fully constructive solution: an…
Penetration of two coupled particles through a repulsive barrier is considered. A simple mechanism of the appearance of barrier resonances is demonstrated that makes the barrier anomalously transparent as compared to the probability of…
We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
The Kullback-Leibler divergence, the Kullback-Leibler variation, and the Bernstein "norm" are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric…
When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave…
Quantum correlations do not allow signalling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signalling condition limits allowed operations…
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom…
Quantum tunneling through a two-dimensional static barrier becomes unusual when a momentum of an electron has a tangent component with respect to a border of the prebarrier region. If the barrier is not homogeneous in the direction…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination…
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
A variational wave function constructed with correlated Hyperspherical Harmonic functions is used to describe the Helium trimer. This system is known to have a deep bound state. In addition, different potential models predict the existence…
It is claimed in another paper that the collapse of a quantum mechanical wave function is more than invariant, it is trans-representational. It must occur along a fully invariant surface. The obvious surface available for this purpose is…
We propose two experimental schemes for quantum state discrimination that achieve the optimal tradeoff between the probability of correct identification and the disturbance on the quantum state.