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We develop the theory of local operations and classical communication (LOCC) for bipartite quantum systems represented by commuting von Neumann algebras. Our central result is the extension of Nielsen...

In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems, but are there different forms of infinite entanglement? To understand entang...

We study convergence rates of the Trotter splitting $$\begin{aligned} e^{A+L} = \lim _{n \rightarrow \infty } \Big (e^{L/n} e^{A/n}\Big )^n \end{aligned}$$ e A + L = lim n → ∞ ( e L / n e A / n ) n in the strong operator topology. In the first part, we use complex interpolation theory to treat generators L and A of contraction semigroups on Banach spaces, with L relatively A-bounded. In the second part, we study unitary dynamics on Hilbert spaces and develop a new technique based on the concept of energy constraints. Our results provide a complete picture of the convergence rates for the Trotter splitting for all common types of Schrödinger and Dirac operators, including singular, confining and magnetic vector potentials, as well as molecular many-body Hamiltonians in dimension $$d=3$$ d = 3 . Using the Brezis-Mironescu inequality, we derive convergence rates for the Schrödinger operator with $$V(x)=\pm |x|^{-a}$$ V ( x ) = ± | x | - a potential. In each case, our conditions are fully explicit.

Embezzlement of entanglement allows to extract arbitrary entangled states from a suitable embezzling state using only local operations while perturbing the resource state arbitrarily little. A natural...

The uniqueness of purifications of quantum states on a system $A$ up to local unitary transformations on a purifying system $B$ is central to quantum information theory. We show that, if the two syste...

Recently Wang et al. have reported a violation of a Bell inequality without entanglement [arXiv:2507.07756]. We show that their result is an artifact of postselection. It is well known that postselect...

Structure theory for measure-preserving systems, additive combinatorics, and correlations of multiplicative functions

Lauritz van Luijk, Alexander Stottmeister, and Henrik Wilming, Quantum 9, 1818 (2025). Embezzlement of entanglement refers to the task of extracting entanglement from an entanglement resource via loca...

Embezzlement of entanglement is an exotic phenomenon in quantum information science, describing the possibility of extracting entanglement from a resource system without changing its quantum state. In...

We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically mean...

Researchers demonstrated that relativistic quantum fields can be "universal embezzlers," extracting quantum states with minimal disturbance

Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system (the ``embezzler'') via local quantum opera...

Some quantum fields that extend throughout all of space-time could be a rich resource of quantum entanglement that can be extracted forever