# Dr. Matthias Kleinmann

PostdocNow at the University of the Basque Country UPV/EHU

## Preprints

See also arxiv

M. Kleinmann
*
Sequences of projective measurements in generalized probabilistic models
*

arXiv:
1402.3583

We define a simple rule to describe sequences of projective measurements for such generalized probabilistic models that can be described by an Archimedean order-unit vector space. For quantum mechanics, this definition yields the established L\"uders's rule, while in the general case it can be seen as the least disturbing or most coherent way to perform sequential measurements. As example we show that Spekkens toy model is an instance of our definition. We also demonstrate the possibility of strong post-quantum correlations and triple-slit correlations for certain non-quantum toy models.

C. Schwemmer, L. Knips, D. Richart, T. Moroder, M. Kleinmann, O. Gühne, H. Weinfurter
*
Systematic errors in current quantum state tomography tools
*

arXiv:
1310.8465

Common tools for obtaining physical density matrices in experimental quantum state tomography lead to systematic errors. For example, using maximum likelihood or free least squares optimization for state reconstruction, we observe systematic underestimation of the fidelity and an overestimation of entanglement. A solution for this problem can be achieved by a linear evaluation of the data yielding consistent and computational simple bounds including error bars.

O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, and J.-Å. Larsson
*
Bounding the quantum dimension with contextuality
*

arXiv:
1302.2266

We show that quantum contextuality is a resource that can be used to certify the dimension of quantum systems. To prove this, we derive the bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. The resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.

## Publications

C. Budroni, T. Moroder, M. Kleinmann, O. Gühne
*
Bounding temporal quantum correlations
*

Phys. Rev. Lett.
*
111
*,
020403
(
2013
),
arXiv:
1302.6223

Sequential measurements on a single particle play an important role in fundamental tests of quantum mechanics. We provide a general method to analyze temporal quantum correlations, which allows us to compute the maximal correlations for sequential measurements in quantum mechanics. As an application, we present the full characterization of temporal correlations in the simplest Leggett-Garg scenario and in the sequential measurement scenario associated with the most fundamental proof of the Kochen-Specker theorem.

Jochen Szangolies, Matthias Kleinmann, Otfried Gühne
*
Tests against noncontextual models with measurement disturbances
*

Phys. Rev. A
*
87
*,
050101(R)
(
2013
),
arXiv:
1303.3837

The testability of the Kochen-Specker theorem is a subject of ongoing controversy. A central issue is that experimental implementations relying on sequential measurements cannot achieve perfect compatibility between the measurements and that therefore the notion of noncontextuality does not apply. We demonstrate by an explicit model that such compatibility violations may yield a violation of noncontextuality inequalities, even if we assume that the incompatibilities merely originate from context-independent noise. We show, however, that this problem can be circumvented by combining the ideas behind Leggett-Garg inequalities with those of the Kochen-Specker theorem.

T. Moroder, M. Kleinmann, P. Schindler, T. Monz, O. Gühne, and R. Blatt
*
Certifying Systematic Errors in Quantum Experiments
*

Phys. Rev. Lett.
*
110
*,
180401
(
2013
),
arXiv:
1204.3644

When experimental errors are ignored in an experiment, the subsequent analysis of its results becomes questionable. We develop tests to detect systematic errors in quantum 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 and present three detection methods: the first two employ linear inequalities while the third is based on the generalized likelihood ratio.

S. Niekamp, T. Galla, M. Kleinmann, O. Gühne
*
Computing complexity measures for quantum states based on exponential families
*

J. Phys. A: Math. Theor.
*
46
*,
125301
(
2013
),
arXiv:
1212.6163

Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be considered as a measure of complexity of a given state. We investigate the resulting optimization problem and show how symmetries can be exploited to simplify the task of finding the nearest thermal state in a given exponential family. We also present an algorithm for the computation of the complexity measure and consider specific examples to demonstrate its applicability.

E. Amselem, M. Bourennane, C. Budroni, A. Cabello, O. Gühne, M. Kleinmann, J.-Å. Larsson, M. Wieśniak
*
Comment on ”State-Independent Experimental Test of Quantum Contextuality in an Indivisible System”
*

Phys. Rev. Lett.
*
110
*,
078901
(
2013
),
arXiv:
1302.0617

We argue that the experiment described in the recent Letter by Zu et al. [Phys. Rev. Lett. 109, 150401 (2012); arXiv:1207.0059v1] does not allow to make conclusions about contextuality, since the measurement of the observables as well as the preparation of the state manifestly depend on the chosen context.

O. Gühne, M. Kleinmann
*
Auf den Kontext kommt es an
*

Physik Journal
*
12(2)
*,
25
(
2013
)

Die Quantenmechanik hat viele, scheinbar paradoxe Konsequenzen. Diese Tatsache hat zu Spekulationen darüber verleitet, ob es eine übergeordnete Theorie geben könnte, die im Einklang mit der klassischen Physik ist. Neben der Bellschen Ungleichung gibt es ein weitreichendes Theorem von Ernst Specker und Simon Kochen, das es ermöglicht, „klassische Modelle“ quantenmechanischer Systeme auszuschließen. Was als Nachdenken über die logische Struktur der Quantenmechanik begann, lässt sich nun auch im Experiment beobachten.

M. Kleinmann, T.J. Osborne, V.B. Scholz, A.H. Werner
*
Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations
*

Phys. Rev. Lett
*
110
*,
040403
(
2013
),
arXiv:
1205.3358

What singles out quantum mechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalization of Dvoretzky’s theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

M. Kleinmann, C. Budroni, J.-A. Larsson,O. Gühne, A. Cabello
*
Optimal Inequalities for State-Independent Contextuality
*

Phys. Rev. Lett.
*
109
*,
250402
(
2012
),
arXiv:
1204.3741

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual correla- tions in a state-independent manner admits an exact solution, as it can be formulated as a linear program. We introduce the noncontextuality polytope as a generalization of the locality polytope and apply our method to identify two different tight optimal inequalities for the most fundamental quantum scenario with state-independent contextuality.

S. Niekamp, M. Kleinmann, and O. Gühne
*
Entropic uncertainty relations and the stabilizer formalism
*

J. Math. Phys.
*
53
*,
012202
(
2012
),
arXiv:
1103.2316

J.-A. Larsson, M. Kleinmann, O. Gühne, and A. Cabello
*
Violating noncontextual realism through sequential measurements
*

AIP Conf. Proc.
*
1327
*,
401
(
2011
)

M. Kleinmann, O. Gühne, J.R. Portillo, J.-A. Larsson, and A. Cabello
*
Memory cost of quantum contextuality
*

New J. Phys.
*
13
*,
113011
(
2011
),
arXiv:
1007.3650

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimum amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information-carrying capacity of the system.

M. Kleinmann, H. Kampermann, and D. Bruß
*
Asymptotically perfect discrimination in the LOCC paradigm
*

Phys. Rev. A
*
84
*,
042326
(
2011
),
arXiv:
1105.5132

We revisit the problem of discriminating orthogonal quantum states within the local-quantum-operation-and-classical-communication (LOCC) paradigm. Our particular focus is on the asymptotic situation where the parties have infinite resources and the protocol may become arbitrarily long. Our main result is a necessary condition for perfect asymptotic LOCC discrimination. As an application, we prove that for complete product bases, unlimited resources are of no advantage. On the other hand, we identify an example for which it still remains undecided whether unlimited resources are superior.

S. Niekamp, M. Kleinmann, and O. Gühne
*
Discrimination strategies for inequivalent classes of multipartite entangled states
*

Phys. Rev. A
*
82
*,
022322
(
2010
),
arXiv:
1006.1313

B. Jungnitsch, S. Niekamp, M. Kleinmann, O. Gühne, H. Lu, W.-B. Gao, Y.-A. Chen, Z.-B. Chen, and Jian-Wei Pan
*
Increasing the statistical significance of entanglement detection in experiments
*

Phys. Rev. Lett.
*
104
*,
210401
(
2010
),
arXiv:
0912.0645

O. Gühne, M. Kleinmann, A. Cabello, J.-Å. Larsson, G. Kirchmair, F. Zähringer, R. Gerritsma, and C.F. Roos
*
Compatibility and noncontextuality for sequential measurements
*

Phys. Rev. A
*
81
*,
022121
(
2010
),
arXiv:
0912.4846

M. Kleinmann, H. Kampermann, D. Bruß
*
Unambiguous discrimination of mixed quantum states: Optimal solution and case study
*

Phys. Rev. A
*
81
*,
020304(R)
(
2010
),
arXiv:
0807.3923

M. Kleinmann, H. Kampermann, D. Bruß
*
Structural approach to unambiguous discrimination of two mixed states
*

J. Math. Phys.
*
51
*,
032201
(
2010
),
arXiv:
0803.1083

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C.F. Roos
*
State-independent experimental test of quantum contextuality
*

Nature
*
460
*,
494
(
2009
),
arXiv:
0904.1655

R. Hübener, M. Kleinmann, T.-C. Wei, C. Gonzalez-Guilen, and O. Gühne
*
The geometric measure of entanglement for symmetric states
*

Phys. Rev. A
*
80
*,
032324
(
2009
),
arXiv:
0905.4822

M. Kleinmann, H. Kampermann, Ph. Raynal, D. Bruß
*
Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination
*

J. Phys. A: Math. Theor.
*
40
*,
F871
(
2007
),
arXiv:
0705.3391

P. Skwara, H. Kampermann, M. Kleinmann, D. Bruß
*
Entanglement witnesses and a loophole problem
*

Phys. Rev. A
*
76
*,
012312
(
2007
),
arXiv:
quant-ph/0608058

M. Kleinmann, H. Kampermann, T. Meyer, D. Bruß
*
Purifying and Reversible Physical Processes
*

Appl. Phys. B
*
86
*,
371
(
2007
),
arXiv:
quant-ph/0608053

T. Meyer, H. Kampermann, M. Kleinmann, D. Bruß
*
Finite key analysis for symmetric attacks in quantum key distribution
*

Phys. Rev. A
*
74
*,
042340
(
2006
),
arXiv:
quant-ph/0607141

M. Kleinmann, H. Kampermann, T. Meyer, D. Bruß
*
Physical Purification of Quantum States
*

Phys. Rev. A
*
73
*,
062309
(
2006
),
arXiv:
quant-ph/0509100

M. Kleinmann, H. Kampermann, D. Bruß
*
Generalization of quantum state comparison
*

Phys. Rev. A
*
72
*,
032308
(
2005
),
arXiv:
quant-ph/0503012