Markus Tiersch

Contact

Institute for Theoretical Physics
University of Innsbruck
Technikerstraße 25
A-6020 Innsbruck, Austria

Institute for Quantum Optics and Quantum Information
Austrian Academy of Sciences
Technikerstraße 21A
A-6020 Innsbruck, Austria

Phone: +43 512 507 4744

markus.tiersch@oeaw.ac.at

Current Status

Postdoctoral Researcher in the Quantum Information Group at UIBK
and in the group Quantum Information and Quantum Computation
headed by Univ.-Prof. Dr. Hans J. Briegel

Publications

[ preprints | peer-reviewed | books | theses ]

Preprints

• A critical view on transport and entanglement in models of photosynthesis

  Markus Tiersch, Sandu Popescu, Hans J. Briegel
  arXiv:1104.3883 [i]

  Quantum effects in biological light-harvesting molecules, such as quantum coherence of excitonic states and entanglement have recently gained much attention. We observe a certain discrepancy between the original experimental work and several theoretical treatments of coherent excitation transport in light-harvesting molecules. Contrary to what is generally stated, we argue that entanglement in such molecules is generally not equivalent to the presence of coherence but mostly introduced by initial assumptions underlying the models, and that entanglement, as opposite to coherence, seems to play no role in the transport efficiency.

• Universality in open system entanglement dynamics

  Markus Tiersch, Fernando de Melo, and Andreas Buchleitner
  arXiv:0810.2506 [i]

  We show that the entanglement evolution of an open quantum system initially prepared in a random pure state – as quantified by a large class of entanglement quantifiers – is universal, in the limit of large Hilbert space dimensions.

Peer-reviewed articles

• Motional effects on the efficiency of excitation transfer

  Ali Asadian, Markus Tiersch, Gian Giacomo Guerreschi,
  Jianming Cai, Sandu Popescu, and Hans J. Briegel
  New Journal of Physics 12, 075019 (2010) [i]

  Included in the Focus Issue on Quantum Effects and Noise in Biomolecules
  DOI: 10.1088/1367-2630/12/7/075019
  arXiv:1002.0346

  Energy transfer plays a vital role in many natural and technological processes. In this work, we study the effects of mechanical motion on the excitation transfer through a chain of interacting molecules with applications to biological scenarios of transfer processes. Our investigation demonstrates that, for various types of mechanical oscillations, the transfer efficiency is significantly enhanced over that of comparable static configurations. This enhancement is a genuine quantum signature and requires the collaborative interplay between the quantum-coherent evolution of the excitation and the mechanical motion of the molecules; it has no analogue in the classical incoherent energy transfer. This effect may not only occur naturally but also be exploited in artificially designed systems to optimize transport processes. As an application, we discuss a simple and hence robust control technique.

• Zero-Transmission Law for Multiport Beam Splitters

  Malte Christopher Tichy, Markus Tiersch, Fernando de Melo,
  Florian Mintert, and Andreas Buchleitner
  Phys. Rev. Lett. 104, 220404 (2010) [i]

  DOI: 10.1103/PhysRevLett.104.220405
  arXiv:1002.5038

  The Hong-Ou-Mandel effect is generalized to a configuration of n bosons prepared in the n input ports of a Bell multiport beam splitter. We derive a strict suppression law for most possible output events, consistent with a generic bosonic behavior after suitable coarse graining.

• Equation of motion for entanglement

  Markus Tiersch, Fernando de Melo, Thomas Konrad, and Andreas Buchleitner
  Quant. Inf. Proc. 8, 523 (2009) [i]

  DOI: 10.1007/s11128-009-0139-4
  arXiv:0909.3317

  We review an evolution equation for quantum entanglement for 2 × 2 dimensional quantum systems, the smallest system that can exhibit entanglement, and extend it to higher dimensional systems. Furthermore, we provide statistical evidence for the equation’s applicability to the experimentally relevant domain of weakly mixed states.

• Detection and typicality of bound entangled states

  Joonwoo Bae, Markus Tiersch, Simeon Sauer, Fernando de Melo,
  Florian Mintert, Beatrix Hiesmayr, and Andreas Buchleitner
  Phys. Rev. A 80, 022317 (2009) [i]

  DOI: 10.1103/PhysRevA.80.022317
  arXiv:0902.4372

  We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states, which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of 3×3 bound entangled states.

• Scalability of Greenberger-Horne-Zeilinger and random-state entanglement in the presence of decoherence

  Leandro Aolita, Daniel Cavalcanti, Antonio Acín, Alejo Salles,
  Markus Tiersch, Andreas Buchleitner, and Fernando de Melo
  Phys. Rev. A 79, 032322 (2009) [i]

  Selected for the Virtual Journal of Nanoscale Science & Technology Vol. 19, Iss. 13 (2009)
  DOI: 10.1103/PhysRevA.79.032322
  arXiv:0812.4203

  We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds and that this discrepancy grows with the number of particles.

• Entanglement evolution in finite dimensions

  Markus Tiersch, Fernando de Melo, and Andreas Buchleitner
  Phys. Rev. Lett. 101, 170502 (2008) [i]

  DOI: 10.1103/PhysRevLett.101.170502
  arXiv:0804.0208

  We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process. The dynamics of the entanglement turns out to be of a simple form and is fully captured by a single quantity.

• Evolution equation for quantum entanglement

  Thomas Konrad, Fernando de Melo, Markus Tiersch,
  Chistian Kasztelan, Adriano Aragao, and Andreas Buchleitner
  Nature Physics 4, 99–102 (2008) [i]

  Published online: 23 December 2007
  DOI: 10.1038/nphys885
  arXiv:0708.0180

  Quantum information technology largely relies on a precious and fragile resource, quantum entanglement, a highly non-trivial manifestation of the coherent superposition of states of composite quantum systems. However, our knowledge of the time evolution of this resource under realistic conditions—that is, when corrupted by environment-induced decoherence—is so far limited, and general statements on entanglement dynamics in open systems are scarce. Here we prove a simple and general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement on passage of either component through an arbitrary noisy channel. The robustness of entanglement-based quantum information processing protocols is thus easily and fully characterized by a single quantity.

• Non-Markovian decoherence in the adiabatic quantum search algorithm

  Markus Tiersch and Ralf Schützhold
  Phys. Rev. A 75, 062313 (2007) [i]

  Selected for the Virtual Journal of Quantum Information Vol. 7, Iss. 6 (2007)
  Selected for the Virtual Journal of Nanoscale Science & Technology Vol. 15, Iss. 25 (2007)
  DOI: 10.1103/PhysRevA.75.062313
  arXiv:quant-ph/0608123

  We consider an adiabatic quantum algorithm (Grover’s search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum algorithm. We find that, under appropriate conditions (such as low temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most important. It turns out that the scalability of the adiabatic quantum algorithm just depends on the infrared behavior of the environment: a reasonably small coupling to the three-dimensional electromagnetic field, for example, does not destroy the scaling behavior, whereas phonons or localized degrees of freedom can be problematic.

• Decoherence versus dynamical Casimir effect

  Ralf Schützhold and Markus Tiersch
  J. Opt. B: Quantum Semiclass. Opt. 7, S120–S125 (2005) [i]

  DOI: 10.1088/1464-4266/7/3/016
  arXiv:quant-ph/0408087

  By means of two simple examples, phase and amplitude damping, the impact of decoherence on the dynamical Casimir effect is investigated. Even without dissipating energy (i.e., pure phase damping), the amount of created particles can be diminished significantly via the coupling to the environment (reservoir theory) inducing decoherence. For a simple microscopic model, it is demonstrated that spontaneous decays within the medium generate those problems; Rabi oscillations are far more advantageous in that respect. These findings are particularly relevant in view of a recently proposed experimental verification of the dynamical Casimir effect.

Edited Books

• 

  Entanglement and Decoherence
  Foundations and Modern Trends

  Andreas Buchleitner, Carlos Viviescas, and Markus Tiersch (Eds.)
  Lecture Notes in Physics, Vol. 768
  Springer (Berlin, Heidelberg, 2009)
  ISBN: 978-3-540-88168-1 [i]

  DOI: 10.1007/978-3-540-88169-8
  Springer online catalogue
  local copy

  About this book

  Entanglement and (de-)coherence arguably define the central issues of concern in present day quantum information theory. Entanglement being a consequence of the quantum mechanical superposition principle for composite systems, a better understanding of the environment-induced destruction of coherent superposition states is required to devise novel strategies for harvesting quantum interference phenomena.

  The present book collects a series of advanced lectures on the theoretical foundations of this active research field, from mathematical aspects underlying quantum topology to mesoscopic transport theory.

  All lectures start out from an elementary level and proceed along a steep learning curve. This makes the material particularly suitable for student seminars on the more fundamental theoretical aspects of quantum information, and equally useful as supplementary reading for advanced lectures on this topic.

Contributions to Books

• 

  Mathematische Grundlagen der Quantenmechanik
  (Mathematical Foundations of Quantum Mechanics)

• Quantencomputer (Quantum Computer)

  Thomas Wellens, Markus Tiersch, and Andreas Buchleitner
  invited book chapters to:
  Taschenbuch der Mathematik (Pocket Book of Mathematics)
  Ilja N. Bronstein, Konstantin A. Semendjajew, Gerhard Musiol, and Heiner Mühlig
  7th Ed., Verlag Harri Deutsch, Frankfurt (Main), Germany, 2008
  1262 pages, Plastic cover, CD-ROM (Version 7.0, 2008)
  ISBN 978-3-8171-2017-8
  Publisher catalogue

Theses

• Benchmarks and Statistics of Entanglement Dynamics

  Ph.D. thesis, Markus Tiersch, University of Freiburg, 2009.
  URL: http://www.freidok.uni-freiburg.de/volltexte/6878/pdf/diss_tiersch_2009.pdf
  Database entry University of Freiburg Document Server [i]

  About this thesis

  In the present thesis we investigate how the quantum entanglement of multicomponent systems evolves under realistic conditions. More specifically, we focus on open quantum systems coupled to the (uncontrolled) degrees of freedom of an environment. We identify key quantities that describe the entanglement dynamics, and provide efficient tools for its calculation. For quantum systems of high dimension, entanglement dynamics can be characterized with high precision.

  In the first part of this work, we derive evolution equations for entanglement. These formulas determine the entanglement after a given time in terms of a product of two distinct quantities: the initial amount of entanglement and a factor that merely contains the parameters that characterize the dynamics. The latter is given by the entanglement evolution of an initially maximally entangled state. A maximally entangled state thus benchmarks the dynamics, and hence allows for the immediate calculation or – under more general conditions – estimation of the change in entanglement. Thereafter, a statistical analysis supports that the derived (in-)equalities describe the entanglement dynamics of the majority of weakly mixed and thus experimentally highly relevant states with high precision.

  The second part of this work approaches entanglement dynamics from a topological perspective. This allows for a quantitative description with a minimum amount of assumptions about Hilbert space (sub-)structure and environment coupling. In particular, we investigate the limit of increasing system size and density of states, i.e. the macroscopic limit. In this limit, a universal behaviour of entanglement emerges following a "reference trajectory", similar to the central role of the entanglement dynamics of a maximally entangled state found in the first part of the present work.

• Nicht-markovsche Dekohärenz im adiabatischen Grover-Suchalgorithmus
  (Non-Markovian Decoherence in the Adiabatic Grover Search Algorithm)

  Diploma thesis, Markus Tiersch, Dresden University of Technology, 2006. [i]

  About this thesis

  The adiabatic quantum computation scheme is a promising candidate for an experimental realization. Decoherence effects are examined using Grover's search algorithm which allows for an analytical treatment and suggests principal decoherence mechanisms for general algorithms which do not allow such a treatment. The weak interaction of quantum computer and reservoir is described with perturbation theory. A leading order criterion for a successfull algorithm is derived from the algorithm dynamics and the reservoir correlation function. A correlation function representing a Markov approximation reproduces the behavior known from the literature, a more general assumption of a stationary reservoir extends the method towards non-Markovian reservoirs with memory effects. Thermal excitations are treated with a stationary-phase approximation, but give only a small contribution for typically large energy gaps in the quantum computer's energy spectrum. Instead, the coupling to low-energy modes of the reservoir with energies of the order of the gap at the avoided level crossing yields the major contributions. The analytical treatment allows for exact expressions in the limit of a large number of qubits, and hence the examination of this quantum computer's scaling behavior. A criterion for the reservoir's spectral function is derived from the smallness condition of the error probability. Typical examples for reservoirs and couplings are examined to determine the feasibility of possible experiments in which they occur.