Inspired by Koashi's complementarity scenario, I'll give an alternative definition of private state in term of an information tradeoff between conjugate bases and then exploit this definition to present a general private state distillation protocol based on CSS codes that achieves the same key rate as recent, more information-theoretic approaches. Additionally, the same method can be used to establish the hashing inequality for entanglement distillation, as well as the direct part of the quantum coding theorem.

I also discuss a generalization of the Maassen-Uffink entropic uncertainty relation, its connection to our new definition of private state and possible applications to security analysis.

If time permits, I will explain how this method circumvent the need of a random permutation for security analysis of a generic QKD protocol.
I will also present how a shield forged from error correction, can be used to improve the key rate of a generic QKD protocol. The shield is actually a system that does not contribute the key, but that is not under the eavesdropper's control. The latter argument is a generalization, from a different perspective, of an observation from Kraus, Branciard and Renner to improve the secret key generation rates of SARG04 by considering a different symmetrization.

This is joint work with Joseph M. Renes.

This is work in progress with Anura Abeyesinghe.

Biography: Avi Zadok received his B.Sc. in Physics and Mathematics at the Hebrew University, Jerusalem in 1994, and the M.Sc. and Ph.D. degrees in Electrical Engineering at Tel-Aviv University in 1999 and 2007. His Ph.D. research areas included dynamic optical filters, statistical optics, optical communications and slow light. He is presently a post-doctoral scholar with the group of prof. Amnon Yariv at Caltech, where his work concentrates on active Silicon photonics and secure optical communications.

Search for topologically non-trivial states of matter has become a important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction [1] of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation [2]. The QSH effect can be generalized to three dimensions as the topological magneto-electric effect (TME) of the topological insulators. I shall also present realistic experimental proposals to observe fractional charge, spin-charge separation and the deconfinement of the magnetic monopoles in these novel topological states of matter.

[1] Bernevig, Hughes and Zhang, Science, 314, 1757, (2006)

[2] Koenig et al, Science 318, 766, (2007)

What is the fastest rate at which a quantum state can be sent between two parties? Here we give the two parties whatever they want -- arbitrary ancillas, side information, entanglement, correlated states, whatever. We show that the rate is equal to the squashed entanglement between the state and reference.

This leads to a more general paradigm for entanglement theory and monogamy based on quantum communication. Note only does it give the squashed entanglement an operational meaning, but also the entanglement of formation and entanglement cost is shown to be the fastest rate at which a quantum state can be sent when the parties have access to side-information which is maximally correlated. A further restriction on the type of side-information implies that the rate of state transmission is given by the quantum mutual information. Furthermore, there is a dual paradigm where one distributes the side-information as maliciously as possible so as to make the sending of the state as difficult as possible. The infamous additivity questions can also be recast and receive an operational interpretation in terms of maximally correlated states.

A quantum network consists of matter nodes to store and process quantum information, optical channels to transport quantum information, and critically, matter-light quantum interfaces between the nodes and the channels that enable efficient distribution of quantum information across the network. Using atomic ensembles as matter nodes, we establish efficient quantum interfaces between atoms and photons based on collective matter-light interactions, and demonstrate some essential capabilities of quantum networks -- generation, storage and distribution of entanglement between remote quantum nodes.

July 23: Group Meeting
      Zhengcheng Gu, MIT
      5:30 pm, 156 Jorgensen    
   
Title:  Tensor-entanglement renormalization group approach to 2D quantum
systems: a unified method for symmetry breaking and topological phase transitions      

Abstract:
Traditional mean-field theory is a simple generic variational approach to calculate various phases. But that approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach with a polynomial computational complexcity for studying 2D quantum phases with long-range entanglement (such as topological phases). Our approach is a variational method that uses tensor product states (also known as projected entangled pair states) as trial wave functions. We use a 2D real space RG algorithm to evaluate expectation values in these wave functions. We demonstrate our algorithm by studying several simple 2D quantum spin models, including both symmetry breaking phase transitions and topological phase transitions.

References:
Closed system case: arXiv:0808.2697
Open system case: Phys. Rev. Lett. 100, 160506 (2008)

December 9: IQI Seminar
      Mohammad Amin, D-Wave Systems
      3:00 pm, 74 Jorgensen   
   
Title:  Spectral gap in adiabatic quantum computation     

Abstract:
A key question regarding the adiabatic quantum computation (AQC) approach to solving NP-hard problems is how the computation time scales with the problem size. Thus far attempts to answer this question have been limited to analytical solutions for very special examples and numerical solutions for small scale problems. However, significant insight can be obtained using well-established results from studies of quantum phase transitions. I will use these concepts to demonstrate that the computation time in AQC shows exponential or polynomial behavior depending on whether the quantum phase transition can be classified as first or second order, respectively. I will discuss both cases in some detail and relate the existence of first order quantum phase transitions to the properties of local minima in a problem Hamiltonian. I will then provide simple examples of the maximum independent set problem, showing agreement between a perturbative theory and numerical calculations.
Finally, I will show experimental results of first order quantum phase transitions in multi-qubit chains of superconducting qubits and compare the results with a quantum mechanical model.