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On Zariski Main Theorem in Algebraic Geometry and Analytic Geometry. We fill a surprising gap of Complex Analytic Geometry by proving the analogue of Zariski Main Theorem in this geometry, i.e. proving that an holomorphic map from an…

We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an…

We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…

By exploiting a generalization of recent results on environment-assisted channel correction, we show that, whenever a quantum system undergoes a channel realized as an interaction with a probe, the more efficiently the information about the…

Let G be a finite subgroup of unitary matrices acting on the space of $N$-qubits. We associate with G a uniform quantum channel QU from the space on $N$-qubits to itself. We give a quantum algorithm to approximate this channel by…

The classical Fubini theorem asserts that the multiple integral is equal to the repeated one for any integrable function on a product measure space. In this paper, we derive an asymptotic variant of the Fubini theorem for maps into…

Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…

We prove that, when two local quantum channels are used paralleled, the quantum-correlating power (QCP) of the composed channel is no less than the sum of QCP of the two channels. For local channels with zero QCP, the super-activation of…

We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every ergodic invariant measure (finite or…

We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of…

We consider a generalisation of Ulam's method for approximating invariant densities of one-dimensional chaotic maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree n which are defined…

The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps…

The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…

We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group $G$ plays a pivotal role in this…

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a…

We prove that closed negatively curved locally symmetric spaces are characterized up to isometry among all homotopy equivalent negatively curved manifolds by the Lyapunov spectra of the periodic orbits of their geodesic flows. This is done…

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…

For a quantum-mechanical counting process we show ergodicity, under the condition that the underlying open quantum system approaches equilibrium in the time mean. This implies equality of time average and ensemble average for correlation…

We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that…

Quantum ergodicity asserts that almost all infinite sequences of eigenstates of a quantized ergodic system are equidistributed in the phase space. On the other hand, there are might exist exceptional sequences which converge to different…