Related papers: Monge Distance between Quantum States
Entangled states of pseudoscalar mesons represent a very interesting tool for studying foundations of quantum mechanics, e.g. for testing Bell inequalities. Recently, they also emerged as a test bench for quantum information protocols. On…
Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…
A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…
We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…
The main goal of quantum metrology is to obtain accurate values of physical parameters using quantum probes. In this context, we show that abstention, i.e., the possibility of getting an inconclusive answer at readout, can drastically…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
We point out a correspondence between classical and quantum states, by showing that for every classical distribution over phase--space, one can construct a corresponding quantum state, such that in the classical limit of $\hbar\to 0$ the…
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…
In this paper we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states $\{\ket{\alpha, \beta}\ |\ \alpha, \beta \in…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
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…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from…
Measuring the quantumness of a system can be done with a variety of methods. In this article we compare different criteria, namely quantum discord, Bell inequality violation and non-separability, for systems placed in a Gaussian state. When…
The distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum…
The concept of entanglement fraction is generalized to define coherence fraction of a quantum state. Precisely, it quantifies the proximity of a quantum state to maximally coherent state and it can be used as a measure of coherence.…
A mesoscopic system of cylindrical geometry made of a metal or a semiconductor is shown to exhibit features of a quantum coherent state. It is shown that magnetostatic interaction can play an important role in mesoscopic systems leading to…
The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it…
Non-locality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Due to non-locality, mixed states of any two subsystems are correlated in a stronger way than what…
We formulate quantum theory taking as a starting point the cone of states.