# Quantum Information and Quantum Entanglement

## Abstracts

**Dagmar Bruss** *(Heinrich-Heine-Universität Düsseldorf, Germany)*

Friday, July 16, 2010**Optimal super dense coding over noisy quantum channels**

We investigate super dense coding in the presence of noise, i.e. the subsystems of the entangled resource state have to pass a noisy unital quantum channel between the sender and the receiver. We discuss explicitly the case of Pauli channels in arbitrary dimension and derive the super dense coding capacity (i.e. the optimal information transfer) for some given resource states. We also study the case that the initial resource state can be chosen: for the qubit depolarizing channel we show that there is a threshold value for the noise parameter, below which the super dense coding protocol is optimized by a maximally entangled initial state, while above the threshold the dense coding capacity for any entangled initial state is smaller than the one for a product state. Finally, we provide an example of a noisy channel where non-unitary pre-processing increases the super dense coding capacity, as compared to only unitary encoding.

**Adan Cabello** *(Universidad de Sevilla, Spain)*

Saturday, July 17, 2010**Recent developments in quantum contextuality**

A physical system is contextual when the result of a measurement on it might depend on which compatible observables were previously measured. We will review some recent developments on this subject:
1. Quantum nonlocality revealed by local contextuality. Two distant systems can violate a Bell inequality even though the correlations between these systems admit a local model. Nonlocality appears when testing extra correlations among successive measurements on one of the systems.
2. Macroscopic state-independent quantum contextuality. For any n-qubit system there is an inequality for the correlations among three compatible dichotomic measurements which is satisfied by any noncontextual theory, but is violated by any quantum state. The violation grows exponentially with n.
3. Memory cost of quantum contextuality. Simulating contextuality requires individual systems to have memory. We show that (log 3)/2 bits of memory per qubit are necessary and sufficient to simulate the results of some recent experiments on quantum contextuality, but one bit per qubit does not suffice if we consider an extended set of observables.

**Marcus Cramer** *(Universität Ulm, Germany)*

Friday, July 16, 2010**Reconstructing quantum states efficiently**

Quantum state tomography has been realized in systems with few components but for larger systems it becomes rapidly infeasible because the number of quantum measurements and computational resources required to process them grow exponentially in the system size. We show that one can do better, gaining an exponential advantage over direct state tomography for quantum states typically realized in Nature. The method is based on matrix product states and makes use of singular value thresholding from compressed sensing. Our results suggest that state tomography of large quantum systems may be much more feasible than the exponential size of state space suggests.

**Marco Piani** *(University of Waterloo, Canada)*

Saturday, July 17, 2010**Entanglement theory where you do not expect it: multipartite violation of Gleason's theorem and stochastic simulation of channels in quantum optics**

Entanglement theory is an important part of quantum information that aims to characterize, quantify and exploit entanglement. Concepts and tools from entanglement theory can find applications in unexpected ways. I will provide evidence for this by presenting two recent results that range from a foundational issue to the simulation of quantum channels in quantum optics. The first one regards what can be considered a violation of Gleason's theorem in the multipartite setting. Roughly speaking, the validity of quantum mechanics at a local level and the non-signalling condition do not imply quantum correlations: counterexamples can be found that are related to multipartite bound entanglement. The second result is a scheme to simulate perfectly but stochastically any quantum channel on a d-rail qudit. We find that the probability of success depends on the entanglement properties of the Choi-Jamiołkowski state isomorphic to the channel.

## Date and Location

**July 16 - 17, 2010**

Max Planck Institute for Mathematics in the Sciences

Inselstraße 22

04103 Leipzig

Germany

see travel instructions

## Scientific Organizers

**Shao-Ming Fei**

Max Planck Institute for Mathematics in the Sciences, Leipzig & School of Mathematical Sciences, Capital Normal University, Beijing

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**Xianqing Li-Jost**

Max Planck Institute for Mathematics in the Sciences

Leipzig

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## Administrative Contact

**Antje Vandenberg**

Max Planck Institute for Mathematics in the Sciences

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