相关论文: Considerations in the Time-Energy Uncertainty Rela…
Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
We study several variations of the question of minimum-error discrimination of thermal states. Besides of providing the optimal values for the probability of error, we also characterize the optimal measurements. For the case of a fixed…
We investigate the ability of a quantum measurement device to discriminate two states or, generically, two hypothesis. In full generality, the measurement can be performed a number $n$ of times, and arbitrary pre-processing of the states…
Given a times series ${\bf Y}$ in $\mathbb{R}^n$, with a piece-wise contant mean and independent components, the twin problems of change-point detection and change-point localization respectively amount to detecting the existence of times…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
This paper studies the optimal state estimation problem for interconnected systems. Each subsystem can obtain its own measurement in real time, while, the measurements transmitted between the subsystems suffer from random delay. The optimal…
We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative…
We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
In continuation of an earlier study, we explore a Neymann-Pearson hypothesis testing scenario where, under the null hypothesis ($\cal{H}_0$), the received signal is a white noise process $N_t$, which is not Gaussian in general, and under…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…
The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time…