相关论文: Recovery and the Data Processing Inequality for qu…

We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight…

Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the…

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 prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…

Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

We show that a relatively simple reasoning using von Neumann entropy inequalities yields a robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC). For entanglement-assisted quantum error-correcting codes…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful…

We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…

We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…

Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the…

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…

In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the…

In this paper, new equivalence theorems for the boundedness of the composition of a quasilinear operator $T$ with the Hardy and Copson operators in weighted Lebesgue spaces are proved. The usefulness of the obtained results is illustrated…

In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lam\'e parameters with certain regularity assumptions. In…

The quantum version of a fundamental entropic data-processing inequality is presented. It establishes a lower bound for the entropy that can be generated in the output channels of a scattering process, which involves a collection of…

We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…

In this work we examine the stability of some classes of integrals, and in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing…