Scientific Presentation SubProject 5: Theory

1. QAP: Scientific Presentation SP5 Scientific Presentation SubProject 5: Theory • Subproject leader: Serge Massar • 20 partners involved • Administrative Structure: • 1 administration workpackage • 6 scientific workpackages

2. QAP: Scientific Presentation SP5 Networking • Informal visits between partners • Workshops • Year 3: no specific Theory workshop • Year 4: • November: Singapore • March: Imperial College

3. Goals : SP5 The aim of SP5 is to develop the general theory of quantum information to provide new insights into the structure and potential of quantum systems for information processing and to develop few qubit applications of QIPC for realistic physical systems studied and developed in other SP1-SP4. We will develop protocols that will show how, using up to 4 qubits, quantum information can be used to solve an outstanding issue in information processing and/or communication with substantial commercial potential and how it can be implemented with technology developed in SP1-SP4.

4. QAP: Scientific Presentation SP5 WP5.1 Algorithms and Complexity • D 5.1.2 Find more quantum algorithms, improved simulation of quantum systems, new relationships among quantum complexity classes, or new classical results that use quantum arguments. • OK

5. QAP: Scientific Presentation SP5 • Quantum Systems that CANNOT be used for Quantum Computation • Noise Thresholds (Kempe, Regev, Unger, de Wolf) • Non Universal sets of gates (Jozsa, Miyake; Yoran) • Too Much Entanglement (Gross, Flammia, Eisert) • Quantum Algorithms • Hidden Subgroup (Ivanyos, Sanselme, Santha) • Superpolynomial speedups based on almost any quantum circuit (Hallgren, Harrow) • “The simplest known protocol, requiring approx 200 qubits, that could be expected to convince a skeptic of the existence of some computational quantum effect.” (D. Shepherd, M. J. Bremner)

6. QAP: Scientific Presentation SP5 WP5.2 Algorithmic Methods • D 5.2.2 Further analysis of existing algorithmic techniques for generating new quantum algorithms • OK

7. QAP: Scientific Presentation SP5 • Quantum Expanders • Ben-Aroya, Schwartz, Ta-Shma • Hastings, Harrow • Interactive Proof Systems • Chailloux and Kerenidis • Random Walks • Magniez, Nayak, Richter, Santha • Approximating Random Unitaries • Harrow, Low

8. QAP: Scientific Presentation SP5 WP5.3 Protocols for Quantum Commerce • D 5.3.2 New protocols for untrusted random numbers generation/amplification • DONE Not yet submitted (Acin, Massar, Pironio)

9. QAP: Scientific Presentation SP5 • QKD • Against Evesdropper limited only by no signalling • Masanes, Renner, Winter, Barrett, Christandl • Based on Bounded Quantum Storage • Damgaard, Fehr, Salvail, Schaffner • Wehner, Schaffner, Terhal • Applications of Extractors to QKD • Ta-Shma • Renner • Quantum Communication Complexity • Regev, de Wolf • Degorre, Kaplan, Laplante, Roland • Chefles

10. QAP: Scientific Presentation SP5 WP5.4 Toolbox for quantum multi-user protocols D 5.4.2 Characterization of correlations in symmetric multipartite states Status??

11. QAP: Scientific Presentation SP5 • Quantification of Entanglement • Entanglement Theory and the Second Law of Thermodynamics, Brandao and Plenio to appear in Nature Physics • Finding Tsirelson Bounds • Navascues, Pironio, Acín • Doherty, Liang, Toner, Wehner • Testing the dimension of Hilbert space • Brunner, Pironio, Acin, Gisin, Methot, Scarani

12. QAP: Scientific Presentation SP5 • Channel Capacities • 6 papers • Simulation of Entanglement with Classical Resources • Brunner, Gisin, Popescu, Scarani • Pre and Post Selection • Popescu, Aharonov, Vaidman • Given a Completely Positive Map, are the underlying dynamics Markovian or non-Markovian • Wolf, Eisert, Cubitt, Cirac

13. lSupersonic Quantum Communication (Eisert, Gross) In spin chains, information propagation occurs at most with speed of sound Travelling wavepacket Detector Local excitation lIn interacting bosonic chains, one can - within a nearest-neighbor translationally invariant model - provably communicate arbitrarily fast! - Exponentially increasing velocity (up to relativistic bounds) at constant classical communication capacity lImplications for fast quantum communication

14. QAP: Scientific Presentation SP5 WP5.5 Architectures • D.5.5.2 Novel architectures for quantum information processing and communication tailored to limitations of available physical systems • OK

15. QAP: Scientific Presentation SP5 • Optimizing design of quantum circuits • Maslov, Falconer, Mosca • Robust and efficient quantum repeaters with atomic ensembles and linear opticsSangouard, Simon, Zhao, Chen, de Riedmatten, Pan, Gisin

16. Optimal Quantum Phase Estimation U. Dorner, R. Demkowicz-Dobrzański, B. J. Smith, J.S. Lundeen, W. Wasilewski, K. Banaszek, I. A. Walmsley phase to be estimated What is the optimal N photons state for phase estimation in the presence of losses? losses If there were no losses the optimal state would be the NOON state NOON states (red curve) are very suceptible to losses. E.g. for 10% losses phase estimation uncertainty grows significantly for N>20 the optimal states (blue curve), yield much lower uncertainty of estimation estimation uncertainty optimal state parameters: number of photons used

17. QAP: Scientific Presentation SP5 WP5.6 Testing Quantum Systems D 5.6.2 Procedures for discrimination of quantum observables. Given Measurement Apparatus A or Apparatus B: Distinguish A from B using finite number of uses of apparatus. • Ziman and Heinosaari, Phys. Rev. A

18. QAP: Scientific Presentation SP5 • Quantum Process TomographyM. Ziman • Quantum benchmarks for the teleportation and storage of squeezed statesOwari, Plenio, Polzik, Serafini, Wolf