Related papers: Shannon theory for quantum systems and beyond: inf…
We show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion of success in transmission, and that which uses the minimum fidelity of pure states in a subspace of…
Entangled qubits transported through space is a key element in many prospective quantum information systems, from long-distance quantum communication to large modular quantum processors. The moving qubits are decohered by time- and…
The uncertainty principle is one of the comprehensive and fundamental concept in quantum theory. This principle states that it is not possible to simultaneously measure two incompatible observatories with high accuracy. Uncertainty…
There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty…
Quantum simulations of fermionic many-body systems crucially rely on mappings from indistinguishable fermions to distinguishable qubits. The non-local structure of fermionic Fock space necessitates encodings that either map local fermionic…
We discuss a general notion of quantum correlations in fermionic or bosonic indistinguishable particles. Our approach is mainly based on the identification of the algebra of single-particle observables, which allows us to devise an…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
Fidelity estimation is essential for the quality control of entanglement distribution networks. Because measurements collapse quantum states, we consider a setup in which nodes randomly sample a subset of the entangled qubit pairs to…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
The entanglement entropy and quantum fidelity in a hard-core-boson model with nearest- and next-nearest-neighbor interactions are studied numerically. By using exact diagonalization and the density matrix renormalization group, the effects…
Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…
Particle number conservation in fermionic systems restricts the allowed local operations on bi-partite systems. We show how this restriction is related to measurement entropy of particle fluctuations and compute it for several regimes of…
To simulate a fermionic system on a quantum computer, it is necessary to encode the state of the fermions onto qubits. Fermion-to-qubit mappings such as the Jordan-Wigner and Bravyi-Kitaev transformations do this using $N$ qubits to…
Review of the probability representation of quantum mechanics and the symplectic tomography approach are presented. The examples of Gaussian states of nanoelectric circuit, Josephson junction, and two interacting high-quality resonant…
Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings…
We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a…