Perimeter Institute Quantum Discussions

This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.

Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

 

Wednesday Oct 24, 2007

We give a convenient representation for any map which is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations.

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Wednesday Oct 17, 2007
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Entanglement plays a fundamental role in quantum information
processing and is regarded as a valuable, fungible resource,
The practical ability to transform (or manipulate) entanglement from one form to another is useful for many applications.
Usually one considers entanglement manipulation of states which are multiple copies of a given bipartite entangled state and requires that the fidelity of the transformation to (or from) multiple copies of
a maximally entangled state approaches unity asymptotically in the

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Wednesday Oct 10, 2007
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It is known that finite fields with d elements exist only when d is a prime or a prime power.
When the dimension d of a finite dimensional Hilbert space is a prime power, we can associate to each basis state of the Hilbert space an element of a finite or Galois field, and construct a finite group of unitary transformations, the generalised Pauli group or discrete Heisenberg-Weyl group. Its elements can be expressed, in terms of the elements of a Galois field.
This group presents numerous

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Wednesday Sep 12, 2007

In this talk we discuss how large classes of classical spin models, such as the Ising and Potts models on arbitrary lattices, can be mapped to the graph state formalism. In particular, we show how the partition function of a spin model can be written as the overlap between a graph state and a complete product state. Here the graph state encodes the interaction pattern of the spin model---i.e., the lattice on which the model is defined---whereas the product state depends only on the couplings of the model, i.e., the interaction strengths.

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Wednesday May 16, 2007
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In nearly every quantum algorithm which exponentially outperforms the best classical algorithm the quantum Fourier transform plays a central role. Recently, however, cracks in the quantum Fourier transform paradigm have begun to emerge. In this talk I will discuss one such development which arises in a new efficient quantum algorithm for the Heisenberg hidden subgroup problem.

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Wednesday Apr 25, 2007

I will survey recent feasibility results on building multi-party cryptographic protocols which manipulate quantum data or are secure against quantum adversaries. The focus will be protocols for secure evaluation of quantum circuits. Along the way, I'll discuss how quantum machines can (and can't) prove knowledge of a secret to a distrustful partner. The talk is based on recent unpublished results, as well as older joint work with subsets of Michael Ben-Or, Claude Crepeau, Daniel Gottesman, and Avinatan Hasidim (STOC '02, FOCS '02, Eurocrypt '05, FOCS '06).

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Wednesday Apr 11, 2007
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Inelastic collisions occur in Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, these processes have not been studied in the case when particles do not escape the trap. We show that such inelastic processes are relevant in quantum properties of the system such as the evolution of the relative population and entanglement. Moreover, including inelastic terms in the models of multimode condensates allows for an exact analytical solution. 

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Wednesday Apr 04, 2007

After a brief overview of the three broad classes of superconducting quantum bits (qubits)--flux, charge and phase--I describe experiments on single and coupled flux qubits. The quantum state of a flux qubit is measured with a Superconducting QUantum Interference Device (SQUID). Single flux qubits exhibit the properties of a spin-1/2 system, including superposition of quantum states, Rabi oscillations and spin echoes.

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Wednesday Mar 28, 2007
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Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is

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Wednesday Mar 21, 2007
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We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication.

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