# AG Eisert

## Quantum many-body theory, quantum information theory, and quantum optics

**Prof. Dr. Jens Eisert**

Dahlem Center for Complex Quantum Systems

Address | Arnimallee 14 Room 1.3.06 14195 Berlin-Dahlem |

Office | Annette Schumann-Welde, Room 1.3.11 |

Telephone | +49-(0)30-838-54781 |

Fax | +49-(0)30-838-53741 |

Email | Prof. Dr. Jens Eisert Annette Schumann-Welde |

**Research**

Our group is concerned with research in quantum information theory, quantum optical implementations of quantum information ideas, and quantum many-body theory.

- We ask what information processing tasks are possible using single quantum systems as carriers of information. On the one hand, we think about the mathematical-theoretical foundations of quantum information, specifically about the theory of entanglement and questions of tomography.
- A main emphasis of our theoretical research is on the theory of quantum systems with many degrees of freedom, particularly in the condensed matter context, concerning their static properties, their efficient numerical simulation, as well as their quantum dynamics in non-equilibrium. Tensor networks play a special role here.
- We are also involved in identifying quantum optical realizations of such ideas, specifically using light modes or cold atoms in optical lattices.

Characteristic for our work is to be guided by the rigor of mathematical physics, but at the same time to be pragmatically and physically motivated, which often leads to collaborations with experimentalists.

Non-equilibrium dynamics of strongly correlated quantum many-body systems

- "Quantum many-body systems out of equilibrium",

Nature Physics 11, 124 (2015). - "Emergence of coherence and the dynamics of quantum phase transitions",

Proceedings of the National Academy of Sciences 112, 3641 (2015). - "Many-body localisation implies that eigenvectors are matrix-product states",

Phys. Rev. Lett. 114, 170505 (2015). - "Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas",

Nature Physics 8, 325 (2012). - "Thermalization in nature and on a quantum computer",

Phys. Rev. Lett. 108, 080402 (2012). - "Absence of thermalization in non-integrable systems",

Phys. Rev. Lett. 106, 040401 (2011). - "A dissipative Church Turing theorem",

Phys. Rev. Lett. 106, 010403 (2011).

**Quantum information theory**

- "Precisely timing dissipative quantum information processing",

Phys. Rev. Lett. 110, 110501 (2013). - "Entangled inputs cannot make imperfect channels perfect",

Phys. Rev. Lett. 106, 230502 (2011). - "Most quantum states are too entangled to be useful as computational resources",

Phys. Rev Lett. 102, 190501 (2009). - "Entanglement combing",

Phys. Rev. Lett. 103, 220501 (2009). - "Entangled families", News and Views,

Nature 455, 180 (2008).

**Quantum system identification, compressed sensing, and tomography**

- "Towards experimental quantum field tomography with ultracold atoms",

Nature Comm. 6, 7663 (2015). - "Extracting dynamical equations from experimental data is NP-hard",

Phys. Rev. Lett. 108, 120503 (2012). - "Quantum tomography via compressed sensing: error bounds, sample complexity, and efficient estimators",

New J. Phys. 14, 095022 (2012). - "Directly estimating non-classicality",

Phys. Rev. Lett. 106, 010403 (2011). - "Quantum state tomography via compressed sensing",

Phys. Rev. Lett. 105, 150401 (2010).

**Tensor network approaches to solving condensed matter models**

- "Entanglement and tensor network states",

Modelling and Simulation 3, 520 (2013). - "Wick's theorem for matrix-product states",

Phys. Rev. Lett. 110, 040401 (2013). - "Solving frustration-free spin models",

Phys. Rev. Lett. 105, 060504 (2010). - "Real-space renormalization yields finite correlations",

Phys. Rev. Lett. 105, 010502 (2010). - "Holographic quantum states",

Phys. Rev. Lett. 105, 260401 (2010). - "Unitary circuits for strongly correlated fermions",

Phys. Rev. A 81, 050303(R) (2010).

**Mathematical physics**

- "Locality of temperature",

Phys. Rev. X 4, 031019 (2014). - "The complexity of relating quantum channels to master equations",

Commun. Math. Phys. 310, 383 (2012). - "Concentration of measure for quantum states with a fixed expectation value",

Commun. Math. Phys. 303, 785 (2011). - "The Gaussian quantum marginal problem",

Commun. Math. Phys. 280, 263 (2008).

**Correlations in condensed-matter systems**

- "Area laws for the entanglement entropy",

Rev. Mod. Phys. 82, 277 (2010).

**Quantum optics**

- "Gaussification and entanglement distillation of continuous-variable systems: A unifying picture",

Phys. Rev. Lett. 108, 020501 (2012). - "Experimental implementation of the optimal linear-optical controlled phase gate",

Phys. Rev. Lett. 106, 013602 (2011). - "Tomography of quantum detectors",

Nature Physics 5, 27 (2009).

**Open quantum systems and opto-mechanics**

- "Observation of non-Markovian micro-mechancial Brownian motion",

Nature Comm. (2015). - "Cooling by heating",

Phys. Rev. Lett. 108, 120602 (2012). - "Gently manipulating opto-mechanical systems",

Phys. Rev. Lett. 103, 213603 (2009). - "Assessing non-Markovian dynamics",

Phys. Rev. Lett. 101, 150402 (2008).

For more recent publications and a complete list of older publications, see this link.