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The main objective of the paper is to unveil an adequate mathematics hidden behind entanglement, that is Geometric Invariant Theory. More specifically relation between these two subjects can be described by the following theses. (i) Total…
In the context of quantifying entanglement we study those functions of a multipartite state which do not increase under the set of local transformations. A mathematical characterization of these monotone magnitudes is presented. They are…
We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two independent harmonic oscillators…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
Quantum information theory is plagued by the problem of regularisations, which require the evaluation of formidable asymptotic quantities. This makes it computationally intractable to gain a precise quantitative understanding of the…
We explore the task of optimal quantum channel identification, and in particular the estimation of a general one parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including…
Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state and call…
An asymptotic entanglement measure for any bipartite states is derived in the light of the dense coding capacity optimized with respect to local quantum operations and classical communications. General properties and some examples with…
We consider parameter estimations with probes being the boundary driven/dissipated non- equilibrium steady states of XXZ spin 1/2 chains. The parameters to be estimated are the dissipation coupling and the anisotropy of the spin-spin…
We derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
We present an improved phase estimation scheme employing entangled coherent states and demon- strate that the states give the smallest variance in the phase parameter in comparison to NOON, BAT and "optimal" states under perfect and lossy…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
Motivated by applications to covert quantum radar, we analyze a covert quantum sensing problem, in which a legitimate user aims at estimating an unknown parameter taking finitely many values by probing a quantum channel while remaining…
Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
The degree of entanglement is determined for an arbitrary state of a broad class of PT-symmetric bipartite composite systems. Subsequently we quantify the rate with which entangled states are generated and show that this rate can be…
Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…