arXiv subjects

Florian Hulpke

Publications and source records attributed to Florian Hulpke.

3 recordsLinked to original sources

arXiv2005

Unitarity as preservation of entropy and entanglement in quantum systems

The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite quantum systems.

quant-ph↗

arXiv2004

A two-way algorithm for the entanglement problem

We propose an algorithm which proves a given bipartite quantum state to be separable in a finite number of steps. Our approach is based on the search for a decomposition via a countable subset of product states, which is dense within all product states. Performing our algorithm simultaneously with the algorithm by Doherty, Parrilo and Spedalieri (which proves a quantum state to be entangled in a finite number of steps) leads to a two-way algorithm that terminates for any input state. Only for a set of arbitrary small measure near the border between separable and entangled states the result is inconclusive.

quant-ph↗

arXiv2004

Simplifying Schmidt number witnesses via higher-dimensional embeddings

We apply the generalised concept of witness operators to arbitrary convex sets, and review the criteria for the optimisation of these general witnesses. We then define an embedding of state vectors and operators into a higher-dimensional Hilbert space. This embedding leads to a connection between any Schmidt number witness in the original Hilbert space and a witness for Schmidt number two (i.e. the most general entanglement witness) in the appropriate enlarged Hilbert space. Using this relation we arrive at a conceptually simple method for the construction of Schmidt number witnesses in bipartite systems.

quant-ph↗