Related papers: Quantum information theory and Fourier multipliers…
We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is…
Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal…
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more…
We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
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…
The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…
Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels,…
We prove that quantum thermal Gaussian input states minimize the output entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are entanglement breaking and of the multi-mode quantum Gaussian phase contravariant channels…
Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we…
Entanglement shared between the two ends of a quantum communication channel has been shown to be a useful resource in increasing both the quantum and classical capacities for these channels. The entanglement-assisted capacities were derived…
Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years. An early result by Morgenstern from 1973, provides an $\Omega(n…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups…
Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as…
In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and…
The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…