# Dr. Tobias Moroder

former PostdocRoom: B-111

Phone: +49 271 740 3716

## Preprints

See also arxiv

T. Moroder, M. Curty, C. C. W. Lim, L. P. Thinh, H. Zbinden, N. Gisin
*
Security of distributed-phase-reference quantum key distribution
*

arXiv:
1207.5544

Distributed-phase-reference quantum key distribution stands out for its easy implementation with present day technology. Since many years, a full security proof of these schemes in a realistic setting has been elusive. For the first time, we solve this long standing problem and present a generic method to prove the security of such protocols against general attacks. To illustrate our result we provide lower bounds on the key generation rate of a variant of the coherent-one-way quantum key distribution protocol. In contrast to standard predictions, it appears to scale quadratically with the system transmittance.

T. Moroder, P. Hyllus, G. Toth, C. Schwemmer, A. Niggebaum, S. Gaile, O. Gühne and H. Weinfurter
*
Permutationally invariant state reconstruction
*

arXiv:
1205.4941

Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.

T. Moroder, M. Kleinmann, P. Schindler, T. Monz, O. Gühne and R. Blatt
*
Detection of systematic errors in quantum experiments
*

arXiv:
1204.3644

When systematic errors are ignored in an experiment, the subsequent analysis of its results becomes questionable. We develop tests to identify systematic errors in experiments where only a finite amount of data is recorded and apply these tests to tomographic data taken in an ion-trap experiment. We put particular emphasis on quantum state tomography experiments and present two detection methods; the first relies on ideas similar to entanglement witnesses or Bell inequalities while the second is based on the generalized likelihood ratio test.

## Publications

T. Moroder and O. Gittsovich
*
Calibration robust entanglement detection beyond Bell inequalities
*

Phys. Rev. A
*
85
*,
032301
(
2012
),
arXiv:
1111.5874

In its vast majority entanglement verification is examined either in the complete characterized or totally device independent scenario. The assumptions imposed by these extreme cases are often either too weak or strong for real experiments. Here we investigate this detection task for the intermediate regime where partial knowledge of the measured observables is known, considering cases like orthogonal, sharp or only dimension bounded measurements. We show that for all these assumptions it is not necessary to violate a corresponding Bell inequality in order to detect entanglement. We derive strong detection criteria that can be directly evaluated for experimental data and which are robust against large classes of calibration errors. The conditions are even capable of detecting bound entanglement under the sole assumption of dimension bounded measurements.

O. Gühne, B. Jungnitsch, T. Moroder, and Y. S. Weinstein
*
Multiparticle entanglement in graph-diagonal states
*

Phys. Rev. A
*
84
*,
052319
(
2011
),
arXiv:
1107.4863

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits.

B. Jungnitsch, T. Moroder, and O. Gühne
*
Entanglement Witnesses for Graph States: General Theory and Examples
*

Phys. Rev. A
*
84
*,
032310
(
2011
),
arXiv:
1106.1114

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.

M. Curty and T. Moroder
*
Heralded qubit amplifiers for practical device-independent quantum key distribution
*

Phys. Rev. A
*
84
*,
010304(R)
(
2011
),
arXiv:
1105.2573

Device-independent quantum key distribution does not need a precise quantum mechanical model of employed devices to guarantee security. Despite its beauty, it is still a very challenging experimental task. We compare a recent proposal by Gisin et al. [Phys. Rev. Lett. 105, 070501 (2010)] to close the detection loophole problem with that of a simpler quantum relay based on entanglement swapping with linear optics. Our full-mode analysis for both schemes confirms that, in contrast to recent beliefs, the second scheme can indeed provide a positive key rate which is even considerably higher than that of the first alternative. The resulting key rates and required detection efficiencies of approximately 95% for both schemes, however, strongly depend on the underlying security proof.

B. Jungnitsch, T. Moroder, and O. Gühne
*
Taming multiparticle entanglement
*

Phys. Rev. Lett.
*
106
*,
190502
(
2011
),
arXiv:
1010.6049

We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite programming and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponentially improved noise robustness compared with existing schemes.