Related papers: Comparing metrics for mixed quantum states: Sjoqvi…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
A framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
A promising practical application of entanglement is metrology, where quantum states can be used to make measurements beyond the shot noise limit. Here we consider how metrology schemes could be realised using atomic Bose-Einstein…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
We consider the interaction of a quantum system (spin-1/2) with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian Master equation show that the…
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the…
The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in…
A geometric interpretation for the A-fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the A-fidelity are studied by numerical method. An…
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…
We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…
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 introduce a simple measure of "classicality" of pure and mixed quantum states as a maximum value of the Hilbert-Schmidt "scalar products" between the renormalized statistical operators of the state concerned and all displaced thermal…
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…