Related papers: Alignment of reference frames and an operational i…
Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates {q} satisfying Hamilton's motion equations will likewise satisfy them when played "backwards", with the corresponding momenta changing signs :…
The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp…
Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries…
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a…
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum…
Quantum states may exhibit asymmetry with respect to the action of a given group. Such an asymmetry of states can be considered as a resource in applications such as quantum metrology, and it is a concept that encompasses quantum coherence…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in…
Symmetry packaging is the phenomenon whereby, upon particle creation, all the internal quantum numbers (IQNs) become locked into a single irreducible representation (irrep) block of the gauge group, as required by locality and gauge…
Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a…
Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain…
Let $\mathbb{H}\trianglelefteq\mathbb{G}$ be a closed normal subgroup of a locally compact quantum group. We introduce a strictly positive group-like element affiliated with $L^{\infty}(\mathbb{G})$ that, roughly, measures the failure of…
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…
Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained…
A Holevo measure is used to discuss how much information about a given POVM on system $a$ is present in another system $b$, and how this influences the presence or absence of information about a different POVM on $a$ in a third system $c$.…
The framework of internal quantum reference frames (QRFs) constitutes a universal toolset for dealing with symmetries in quantum theory and has led to new revelations in quantum gravity, gauge theories and foundational physics. Multiple…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
Quantum resources such as entanglement, information redundancy, and coherence enable revolutionary advantages but obey fundamental tradeoffs. We present a unified geometric constraint governing three core operational tasks: teleportation…
A conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given…