8 papers
Sufficient positive maps between von Neumann algebras: Rényi divergences
Anna Jenčová, Lauritz van Luijk
We prove recovery theorems for - Rényi divergences under normal unital positive maps between von Neumann algebras. Previous results in this setting required 2-positivity, whi…
Quantum steering is equivalent to state-preserving conditional expectations
Lauritz van Luijk, Amine Marrakchi, Tobias Osborne +2
In systems with infinitely many degrees of freedom, fundamental results from quantum information theory can fail. An important example is the uniqueness of purifications: Even when…
Sufficiency and Petz recovery for positive maps
Lauritz van Luijk, Henrik Wilming
We study the interconversion of families of quantum states ("statistical experiments") via positive, trace-preserving (PTP) maps and clarify its mathematical structure in terms of…
Uniqueness of purifications is equivalent to Haag duality
Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming
The uniqueness of purifications of quantum states on a system up to local unitary transformations on a purifying system is central to quantum information theory. We show th…
Heisenberg-smooth operators from the phase space perspective
Robert Fulsche, Lauritz van Luijk
Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof o…
Critical Fermions are Universal Embezzlers
Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming
Universal embezzlers are bipartite quantum systems from which any entangled state may be extracted to arbitrary precision using local operations while perturbing the state of the s…