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Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information…
I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
Generalized relative entropy, monotone Riemannian metrics, geodesic distance, and trace distance are all known to decrease under the action of quantum channels. We give some new bounds on, and relationships between, the maximal contraction…
We present a family of easily computable upper bounds for the Holevo quantity of ensemble of quantum states depending on a reference state as a free parameter. These upper bounds are obtained by combining probabilistic and metric…
A fundamental question in information theory is to quantify the loss of information under a noisy channel. Partial orders and contraction coefficients are typical tools to that end, however, they are often also challenging to evaluate. For…
By considering quantum computation as a communication process, we relate its efficiency to a communication capacity. This formalism allows us to rederive lower bounds on the complexity of search algorithms. It also enables us to link the…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
Numerically solving partial differential equations is a ubiquitous computational task with broad applications in many fields of science. Quantum computers can potentially provide high-degree polynomial speed-ups for solving PDEs, however…
The strengthened data processing inequality have been proved. The general theory have been illustrated on the simple example.
We discuss how to use the recent progress in understanding of the $x$-$y$ duality and symplectic duality in the theory of topological recursion and its generalizations in order to efficiently compute the quantum spectral curve operators for…
Quantum computing promises speedup of classical algorithms in the long term. Current hardware is unable to support this goal and programs must be efficiently compiled to use of the devices through reduction of qubits used, gate count and…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
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…
Quantum states naturally decay under noise. Many earlier works have quantified and demonstrated lower bounds on the decay rate, showing exponential decay in a wide variety of contexts. Here we study the converse question: are there uniform…
We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well known Shannon lower bound in a variety of instances of rate-distortion…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…