printlogo
http://www.ethz.ch/index_EN
Welcome
 
print
  

Christandl, Matthias, Prof. Dr.

Matthias Christandl

ETH Zürich
Prof. Dr. Matthias Christandl
Institut f. Theoretische Physik
HIT K 33.4
Wolfgang-Pauli-Str. 27
8093 Zuerich

Phone: +41 44 633 25 92
E-Mail: 

Quantum Information Theory at ETH Zürich

Click here for the joint homepage of the research groups of Prof. Matthias Christandl and Prof. Renato Renner.

Prezis

All my prezis can be found here.

Presentations

Online Tools

Supervised Theses

Publications (year descending)

52 records found

Title Author(s) Year
Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information Details
M. Walter; B. Doran; D. Gross; M. Christandl 2013
Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
Type Journal Article
Author M. Walter; B. Doran; D. Gross; M. Christandl
Year 2013
Journal Science
Abstract Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating any given class of entanglement with an entanglement polytope—a geometric object that characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement and can be generalized to states affected by low levels of noise.
Pages 1205-1208
Volume 340
Issue 6137
Electronic Resource Number 10.1126/science.1232957
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

Pinning of Fermionic Occupation Numbers Details
C. Schilling; D. Gross; M. Christandl 2013
Pinning of Fermionic Occupation Numbers
Type Journal Article
Author C. Schilling; D. Gross; M. Christandl
Year 2013
Journal Physical Review Letters
Abstract The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.
Pages 040404
Volume 110
Issue 4
Electronic Resource Number 10.1103/PhysRevLett.110.040404
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

A hierarchy of topological tensor network states Details
O. Buerschaper; J. M. Mombelli; M. Christandl; M. Aguado 2013
A hierarchy of topological tensor network states
Type Journal Article
Author O. Buerschaper; J. M. Mombelli; M. Christandl; M. Aguado
Year 2013
Journal Journal of Mathematical Physics
Abstract We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the hierarchy we identify ground states of new topological lattice models extending Kitaev's quantum double models [Ann. Phys. 303, 2 (2003)]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing an entanglement renormalization flow. Furthermore, we argue that the hierarchy states are related to each other by the condensation of topological charges.
Pages 012201
Volume 54
Issue 1
Electronic Resource Number 10.1063/1.4773316
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

Reliable Quantum State Tomography Details
M. Christandl; R. Renner 2012
Reliable Quantum State Tomography
Type Journal Article
Author M. Christandl; R. Renner
Year 2012
Journal Physical Review Letters
Abstract Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic limits, the estimates computed by standard methods do not in general coincide with the true state and, therefore, have no operational significance unless their accuracy is defined in terms of error bounds. Here we show that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions—a concept originating from classical statistics. Confidence regions are subsets of the state space in which the true state lies with high probability, independently of any prior assumption on the distribution of the possible states. Our method for computing confidence regions can be applied to arbitrary measurements including fully coherent ones; it is practical and particularly well suited for tomography on systems consisting of a small number of qubits, which are currently in the focus of interest in experimental quantum information science.
Pages 120403
Volume 109
Issue 12
Electronic Resource Number 10.1103/PhysRevLett.109.120403
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

Recoupling Coefficients and Quantum Entropies Details
M. Christandl; M. B. Sahinoglu; M. Walter 2012
Recoupling Coefficients and Quantum Entropies
Type Online Database
Author M. Christandl; M. B. Sahinoglu; M. Walter
Year 2012
Abstract In this work, we show that the asymptotic limit of the recoupling coefficients of the symmetric group is characterized by the existence of quantum states of three particles with given eigenvalues for their reduced density matrices. This parallels Wigner's observation that the semiclassical behavior of the 6j-symbols for SU(2)---fundamental to the quantum theory of angular momentum---is governed by the existence of Euclidean tetrahedra. We explain how to deduce solely from symmetry properties of the recoupling coefficients the strong subadditivity of the von Neumann entropy, first proved by Lieb and Ruskai, and discuss possible generalizations of our result.
URL Link to Website / File
Name of Database arXiv.org

      Export: EndNote XML · BibTex

Entanglement of the Antisymmetric State Details
M. Christandl; N. Schuch; A. Winter 2012
Entanglement of the Antisymmetric State
Type Journal Article
Author M. Christandl; N. Schuch; A. Winter
Year 2012
Journal Communications in Mathematical Physics
Abstract We analyse the entanglement of the antisymmetric state in dimension d × d and present two main results. First, we show that the amount of secrecy that can be extracted from the state is low, more precisely, the distillable key is bounded by O(1/d). Second, we show that the state is highly entangled in the sense that a large number of ebits are needed in order to create the state: entanglement cost is larger than a constant, independent of d. The second result is shown to imply that the regularised relative entropy with respect to separable states is also lower bounded by a constant. Finally, we note that the regularised relative entropy of entanglement is asymptotically continuous in the state. Elementary and advanced facts from the representation theory of the unitary group, including the concept of plethysm, play a central role in the proofs of the main results.
Pages 397-422
Volume 311
Issue 2
Electronic Resource Number 10.1007/s00220-012-1446-7
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

Computing Multiplicities of Lie Group Representations Details
M. Christandl; B. Doran; M. Walter 2012
Computing Multiplicities of Lie Group Representations
Type Conference Proceedings
Author M. Christandl; B. Doran; M. Walter
Year of Conference 2012
Conference Name IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS)
Abstract For fixed compact connected Lie groups H⊆G, we provide a polynomial time algorithm to compute the multiplicity of a given irreducible representation of H in the restriction of an irreducible representation of G. Our algorithm is based on a finite difference formula which makes the multiplicities amenable to Barvinok's algorithm for counting integral points in polytopes. The Kronecker coefficients of the symmetric group, which can be seen to be a special case of such multiplicities, play an important role in the geometric complexity theory approach to the P vs. NP problem. Whereas their computation is known to be #P-hard for Young diagrams with an arbitrary number of rows, our algorithm computes them in polynomial time if the number of rows is bounded. We complement our work by showing that information on the asymptotic growth rates of multiplicities in the coordinate rings of orbit closures does not directly lead to new complexity-theoretic obstructions beyond what can be obtained from the moment polytopes of the orbit closures. Nonasymptotic information on the multiplicities, such as provided by our algorithm, may therefore be essential in order to find obstructions in geometric complexity theory.
Pages 639 - 648
Conference Location New Brunswick, NJ
Electronic Resource Number 10.1109/FOCS.2012.43
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

Eigenvalue Distributions of Reduced Density Matrices Details
M. Christandl; B. Doran; S. Kousidis; M. Walter 2012
Eigenvalue Distributions of Reduced Density Matrices
Type Online Database
Author M. Christandl; B. Doran; S. Kousidis; M. Walter
Year 2012
Abstract Given a random quantum state of multiple (distinguishable or indistinguishable) particles, we provide an algorithm, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced density matrices, and hence some associated physical invariants of the state.
As a corollary, by taking the support of this probability distribution, which is a convex polytope, we recover a complete solution to the one-body quantum marginal problem, i.e., the problem of characterizing the one-body reduced density matrices that arise from some multi-particle quantum state. In the fermionic instance of the problem, which is known as the one-body N-representability problem, the famous Pauli principle amounts to one linear inequality in the description of the convex polytope. We obtain the probability distribution by reducing to computing the corresponding distribution of diagonal entries (i.e., to the quantitative version of a classical marginal problem), which is then determined algorithmically. This reduction applies more generally to symplectic geometry, relating invariant measures for a compact Lie group action to that for the maximal torus action; we state and prove our results in this more general symplectic setting. Our approach is in striking contrast to the existing solution to the computation of the supporting polytope by Klyachko and by Berenstein and Sjamaar, which made crucial use of non-Abelian features. In algebraic geometry, Duistermaat-Heckman measures correspond to the asymptotic distribution of multiplicities of irreducible representations in the associated coordinate ring. In the case of the one-body quantum marginal problem, these multiplicities include bounded height Kronecker and plethysm coefficients. A quantized version of the Abelianization procedure provides an efficient algorithm for their computation.
URL Link to Website / File
Name of Database arXiv.org

      Export: EndNote XML · BibTex

Complete Insecurity of Quantum Protocols for Classical Two-Party Computation Details
H. Buhrman; M. Christandl; C. Schaffner 2012
Complete Insecurity of Quantum Protocols for Classical Two-Party Computation
Type Journal Article
Author H. Buhrman; M. Christandl; C. Schaffner
Year 2012
Journal Physical Review Letters
Abstract A fundamental task in modern cryptography is the joint computation of a function which has two inputs, one from Alice and one from Bob, such that neither of the two can learn more about the other’s input than what is implied by the value of the function. In this Letter, we show that any quantum protocol for the computation of a classical deterministic function that outputs the result to both parties (two-sided computation) and that is secure against a cheating Bob can be completely broken by a cheating Alice. Whereas it is known that quantum protocols for this task cannot be completely secure, our result implies that security for one party implies complete insecurity for the other. Our findings stand in stark contrast to recent protocols for weak coin tossing and highlight the limits of cryptography within quantum mechanics. We remark that our conclusions remain valid, even if security is only required to be approximate and if the function that is computed for Bob is different from that of Alice.
Pages 160501
Volume 109
Issue 16
Electronic Resource Number 10.1103/PhysRevLett.109.160501
URL Link to Website / File
 Link to Website / File

      Export: EndNote XML · BibTex

Entanglement Cost of Quantum Channels Details
M. Berta; F. Brandao; M. Christandl; S. Wehner 2012
Entanglement Cost of Quantum Channels
Type Conference Proceedings
Author M. Berta; F. Brandao; M. Christandl; S. Wehner
Year of Conference 2012
Publisher IEEE
Conference Name IEEE International Symposium on Information Theory
Abstract A natural question in characterizing the information theoretic power of quantum channels is to ask at what rate entanglement is needed in order to asymptotically simulate a quantum channel in the presence of free classical communication. We call this the entanglement cost of a channel, and prove a formula describing it for all channels. We discuss two applications. Firstly, we are able to link the security in the noisy-storage model to a problem of sending quantum rather than classical information through the adversary's storage device. This not only greatly improves the range of parameters where security could be shown previously, but allows us to prove security for storage devices for which no non-trivial statements were known before. Secondly, our result has consequences for the study of the strong converse quantum capacity. Here, we show that any coding scheme that sends quantum information through a quantum channel at a rate larger than the entanglement cost of the channel has an exponentially small fidelity.
Pages 900
Series Title ISIT Proceedings
Conference Location Boston
Electronic Resource Number 10.1109/ISIT.2012.6284692
URL Link to Website / File

      Export: EndNote XML · BibTex

Show all publications.

 

Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne graphische Elemente dargestellt. Die Funktionalität der Website ist aber trotzdem gewährleistet. Wenn Sie diese Website regelmässig benutzen, empfehlen wir Ihnen, auf Ihrem Computer einen aktuellen Browser zu installieren. Weitere Informationen finden Sie auf
folgender Seite.

Important Note:
The content in this site is accessible to any browser or Internet device, however, some graphics will display correctly only in the newer versions of Netscape. To get the most out of our site we suggest you upgrade to a newer browser.
More information

© 2014 ETH Zurich | Imprint | Disclaimer | 16 September 2013
top