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2006 October

Archive for October, 2006

Quantum Metrology – Part 2

Friday, October 13th, 2006

Date: Tuesday 17th October

Who: Animesh Datta

Seminar type: Tutorial Seminar

Time: 4-5pm

Where: Conference Room

Abstract:
Part 2 will deal with the problem of reference frame alignment, which can be seen as an instance of parameter estimation in $\mathrm{SU}(2).$ We will look at some of the methods involved and discuss the results of the analysis. In particular, we will compare the form of the states that achieve the Heisenberg limits in the two problems: clock synchronization and reference frame alignment.

Entanglement and the power of one qubit

Thursday, October 12th, 2006

Date: Friday 13th October

Who: Animesh Datta

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:
The “power of one qubit” refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of n , for all bipartite divisions of the n+1 qubits, and so becomes, when n is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.

Quantum Metrology 1

Monday, October 9th, 2006

Date: Tuesday 10 October

Who: Animesh Datta

Seminar type: Tutorial Seminar

Time 4-5pm

Where: Conference Room

Abstract:
Part 1 of this tutorial will involve the basics of quantum enhanced metrology and the problem of clock synchronization. We will also talk about the general framework of attaining the Heisenberg limit and end with some comments on exponentially enhanced metrology.

The Sound of Inflation: Phonon Correlations in a Chirped Ion Trap

Wednesday, October 4th, 2006

Date: Friday 6th October

Who: Nick Menicucci

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract:

The inflationary hypothesis purports to solve several fundamental problems with standard cosmology, including the anisotropy of the cosmic microwave background (CMB). It is argued that quantum fluctuations in the original state of the universe get “frozen out”

during inflation and become classical density fluctuations, which are believed to be the seeds for galaxies and other structure in the universe.

The physical mechanism by which this “freezing out” actually occurs, though, remains a mystery. Ion traps provide a manageable system with which we can study the acoustic analogues of inflationary processes, including the supposed “freezing out” of quantum fluctuations. Phonons play the role of a discretized quantum field, while the overall trap frequency can be chirped to reproduce the effect of an expanding spacetime. The ions’ electronic states are a classically observable field that is coupled to the phonon field through an external laser. Using standard quantum mechanics, spatial correlations in the detected excitation of electronic states can be shown to be a function of quantum correlations in the initial state of the phonon field. This is work in progress with Gerard Milburn. No prior knowledge of cosmology is assumed.

Can the Born rule be derived?

Tuesday, October 3rd, 2006

Date: Friday 29th September

Topic: Can the Born rule be derived?

Who:Max Schlosshauer

Seminar type: Research Seminar

Time: 12 Midday

Where: Interaction Room

Abstract: The Born rule for quantum probabilities is one of the core postulates of quantum mechanics. In fact, it constitutes *the* link for relating the abstract formalism of QM to experimental data. Wouldn’t it be nice if we could somehow derive the Born rule, instead of having to simply postulate it? I will give an informal overview of some attempts towards such a derivation. In particular, I will discuss an approach recently presented by Zurek, and I will outline some of my own (as well as other people’s) criticisms of this approach.