Related papers: On the Quantumness of a Hilbert Space
The notions of qubits and coherent states correspond to different physical systems and are described by specific formalisms. Qubits are associated with a two-dimensional Hilbert space and can be illustrated on the Bloch sphere. In contrast,…
Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more…
We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or…
We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a…
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as…
Two measures of sensitivity to eavesdropping for alphabets of quantum states were recently introduced by Fuchs and Sasaki in quant-ph/0302092. These are the accessible fidelity and quantumness. In this paper we prove an important property…
When applied to different input states, an imperfect quantum operation yields output states with varying fidelities, defined as the absolute square of their overlap with the desired states. We present an expression for the distribution of…
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…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…
Quantum fidelity is one of the most important measures of similarity between mixed quantum states. However, the usual formulation is cumbersome and hard to understand when encountering the first time. This work shows in a novel, elegant…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…