arXiv subjects

Karl Gerd H. Vollbrecht

Publications and source records attributed to Karl Gerd H. Vollbrecht.

7 recordsLinked to original sources

arXiv2011

Entanglement distillation by dissipation and continuous quantum repeaters

Even though entanglement is very vulnerable to interactions with the environment, it can be created by purely dissipative processes. Yet, the attainable degree of entanglement is profoundly limited in the presence of noise sources. We show that distillation can also be realized dissipatively, such that a highly entanglement steady state is obtained. The schemes put forward here display counterintuitive phenomena, such as improved performance if noise is added to the system. We also show how dissipative distillation can be employed in a continuous quantum repeater architecture, in which the resources scale polynomially with the distance.

quant-ph↗

arXiv2008

On entropy growth and the hardness of simulating time evolution

The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix Product States (MPS), their time evolution can encode quantum computations, so that simulating the latter should be hard classically. However, one might believe that for systems with high enough symmetry, and thus insufficient parameters to encode a quantum computation, efficient classical simulation is possible. We discuss supporting evidence to the contrary: We provide a rigorous proof of the observation that a time independent local Hamiltonian can yield a linear increase of the entropy when acting on a product state in a translational invariant framework. This criterion has to be met by any classical simulation method, which in particular implies that every global approximation of the evolution requires exponential resources for any MPS based method.

quant-ph↗

arXiv2004

Interpolation of recurrence and hashing entanglement distillation protocols

We construct new entanglement distillation protocols by interpolating between the recurrence and hashing protocols. This leads to asymptotic two-way distillation protocols, resulting in an improvement of the distillation rate for all mixed Bell diagonal entangled states, even for the ones with very high fidelity. We also present a method how entanglement-assisted distillation protocols can be converted into non-entanglement-assisted protocols with the same yield.

quant-ph↗

arXiv2002

Conditional entropies and their relation to entanglement criteria

We discuss conditional Renyi and Tsallis entropies for bipartite quantum systems of finite dimension. We investigate the relation between the positivity of conditional entropies and entanglement properties. It is in particular shown that any state having a negative conditional entropy with respect to any value of the entropic parameter is distillable since it violates the reduction criterion. Moreover we show that the entanglement of Werner states in odd dimensions can neither be detected by entropic criteria nor by any other spectral criterion.

quant-ph↗

arXiv2002

Activating NPPT distillation with an infinitesimal amount of bound entanglement

We show that bipartite quantum states of any dimension, which do not have a positive partial transpose, become 1-distillable when one adds an infinitesimal amount of bound entanglement. To this end we investigate the activation properties of a new class of symmetric bound entangled states of full rank. It is shown that in this set there exist universal activator states capable of activating the distillation of any NPPT state.

quant-ph↗

arXiv2001

Distillability via protocols respecting the positivity of partial transpose

We show that all quantum states that do not have a positive partial transpose are distillable via channels, which preserve the positivity of the partial transpose. The question whether NPT bound entanglement exist is therefore closely related to the connection between the set of separable superoperators and PPT-preserving maps.

quant-ph↗

arXiv2000

The Entanglement of Formation for Isotropic States

We give an explicit expression for the entanglement of formation for isotropic density matrices in arbitrary dimensions in terms of the convex hull of a simple function. For two qutrit isotropic states we determine the convex hull and we have strong evidence for its exact form for arbitrary dimension. Unlike for two qubits, the entanglement of formation for two qutrits or more is found to be a nonanalytic function of the maximally entangled fraction in the regime where the density matrix is entangled.

quant-ph↗