Related papers: Equivariant relative submajorization
Let $S(H)$ be the set of all self-adjoint bonded linear operators on $H$ and $\mathcal{V} \subset S(H)$ a subset that is pertinent in mathematical foundations of quantum mechanics. A symmetry is a bijective map $\phi :\mathcal{V} \to…
We revisit Royen's proof of the Gaussian correlation inequality from a supersymmetric point of view. Many key elements in Royen's proof of this inequality have natural geometric interpretations in terms of supersymmetric dimensional…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
Recently, some attention has been given to the so-called Page-Wootters mechanism of quantum clocks. Among the various proposals to explore the mechanism using more modern techniques, some have chosen to use a quantum information…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational…
It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work,…
We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by…
Every clock is a physical system and thereby ultimately quantum. A naturally arising question is how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related.…
Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over…
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics…
A large class of isolated quantum system in a pure state can equilibrate and serve as a heat bath. We show that once the equilibrium is reached, any of its subsystems that is much smaller than the isolated system is thermalized such that…
We give a simple and complete picture on the classification of relative Cuntz--Pimsner algebras (and so also of gauge-equivariant representations) using their intuitive parametrisation by kernel--covariance pairs.
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
We show that in an asymptotically flat space where an S-Matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct super-selection sectors,…
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…