Related papers: Connections and Metrics Respecting Standard Purifi…
Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to a given basis. We first use two of these, the l_1-norm and relative entropy measures, to investigate tradeoffs between the…
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric…
In quantum information theory, communication capacities are mostly given in terms of entropic formulas. Continuity of such entropic quantities are significant, as they ensure uniformity of measures against perturbations of quantum states.…
We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric on the space of density matrices as the complexity measure. Due to Uhlmann's theorem, we…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
Standard Quantum Physics states that the outcome of measurements for some distant entangled subsystems are instantaneously statistically correlated, whatever their mutual distance. This correlation presents itself as if there were a…
In this article we completely describe the existence of canonical metrics, known as optimal symplectic connections, on isotrivial K\"ahler fibrations. In this setting an optimal symplectic connection is induced from a Hermite--Einstein…
We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…
Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality via local operations and classical…
We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…
Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum…
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…
Pseudo-Riemannian metrics with Levi-Civita connection in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the maximal rank solutions of a certain overdetermined projectively…
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
Purification is a process in which decoherence is partially reversed by using several input systems which have been subject to the same noise. The purity of the outputs generally increases with the number of input systems, and decreases…
We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such…
Tiling spaces are constructed using a metric in which two tilings of $\mathbb{R}^n$ are close if and only if, after a small translation, they agree on a large ball around the origin. We construct analogous spaces to study random…
Quantum properties of the state associated to the gluon Green's function in the BFKL approach are studied using a discretization in virtuality space. Considering the coupling constant as imaginary, its density matrix corresponds to a pure…