Talks

We introduce the concept of tight POVMs. In analogy with tight frames, these are POVMs that are as close as possible to orthonormal bases for the space they span. We show that tight rank-one POVMs define the exact class of optimal measurements for linear tomography of quantum states. In this setting they are equivalent to complex projective 2-designs. We also show that tight POVMs define the optimal class of measurements on the probe state for ancilla-assisted process tomography of unital channels. In this setting they are equivalent to unitary 2-designs.

The basic principles of quantum state tomography were first outlined by Stokes for the context of light polarisation more than 150 years ago. For an experimentalist the goal is clear: to use a series of measurement outcomes to make the best possible estimate of a system\'s quantum state, including phase information, with the least amount of measurement (and analysis) time and, if possible, also the least expensive and complicated apparatus. However, although the general ideas are straightforward, there is still much flexibility of choice in the practical details of how to implement tomography in the laboratory - details which may substantially influence the tomographic performance. For example, how do I make my measurements? How do I analyse my data? How confident can I be of my reconstruction anyway? Say, for example, I\'ve made my measurements and taken my data and I\'m now faced with two different ways, essentially equivalent at first glance, of analysing my data, where one way gives me \'better numbers\', e.g., a state with higher entanglement. Which do I choose? One may lead to a higher chance of a successful publication, but this is hardly a satisfactory way of making the decision. The perspective of an experimentalist motivates a fairly pragmatic approach to choosing the best technique for performing tomography. Does it work? How well? Can it work better? In this talk, I will use this approach and discuss issues which arise at each stage of the tomography process, using both numerical and real lab data to characterise the performance quality.

We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction, but also a covariance matrix expressing the measurement uncertainties in a complete way. From this covariance matrix the error bars on any derived quantity can be easily calculated. This is a first step towards the broader goal of devising an omnibus reconstruction method that could be adapted to any tomographic setup with little effort and that treats measurement uncertainties in a statistically well-founded way. We restrict ourselves to the important subclass of tomography based on measurements with discrete outcomes (as opposed to continuous ones), and we also ignore any measurement imperfections (dark counts, less than unit detector efficiency, etc.), which will be treated in further work. We illustrate the general theory on two real tomography experiments of quantum optical information processing elements.

The experimental realization of entangled states requires tools for characterizing the produced states as well as the processes used for creating the entanglement. In my talk, I will present examples of quantum measurements occuring in trapped ion experiments aiming at creating high-fidelity quantum gates.

A new approach to Quantum Estimation Theory will be introduced, based on the novel notions of \'quantum comb\' and \'quantum tester\', which generalize the customary notions of \'channel\' and \'POVM\' [PRL 101 060401 (2008)]. The new approach opens completely new possibilities of optimization in Quantum Estimation, beyond the classic approach of Helstrom and Holevo. Using comb theory it is possible to optimize the input-output arrangement of the black boxes for estimation with many uses. In this way it is possible to prove equivalence of arrangements for optimal estimation of unitaries, and the need of memory assisted protocols for for optimal discrimination of memory channels [arXive:0806.1172]. This also leads to a new notion of distance for channels with memory. Using the theory of quantum testers the optimal tomography schemes are derived---both state and for channel tomography---for arbitrary prior ensemble and arbitrary representation [arXive:0803.3237]. Finally, using the method of generalized pseudo-inverse for optimal data-processing [PRL. 98 020403 (2007)], we derived two improved data-processing for quantum tomography: Adaptive Bayesian and Frequentist [arXive:0807.5058].

The fundamentally different localization concepts of QT, i.e. the Born-(Newton-Wigner) localization of (relativistic) QM as compared with the causal localization (modular localization) of QFT, lead to significant differences in the nature of local observables and affiliated states. This in turn results in a rather sharp distinction between a tensor-factorization and information-theoretic entanglement in QM on the one hand, and a more radical \"thermal entanglement” responsible for an area law for localization entropy. These surprising differences can be traced back to the very different nature of the localized operator algebras in QFT: they are all isomorphic (independent of the localization region) to one abstract \"monad\" (borrowing terminology from Leibniz) and the full reality of QFT (including its symmetries) is contained in the positioning of a finite rather small number (2 for chiral theories, 6 for d=1+3,...) within a joint Hilbert space. It is an important open question to what extend such positional characterizations (where the individual monads are void of any physical properties which reside fully in their relative placements) can be generalized to CST or QG.

In the 1980’s when Vera Rubin was analyzing how stars in galaxies revolve around the galactic core, she made an incredible discovery. The stars where moving much faster than anyone expected. This discovery helped open up a door in physics whose implications are far stranger than the best plot in any science fiction movie. Join us as we explore the mystery of dark matter.

The reason cosmologists have a job is that the Universe as a whole -- the stuff between planets and stars and galaxies -- is, despite first appearances, a pretty interesting place. The strangest fact about it is that it\'s expanding, and always has been, as far as we know (and though Einstein\'s theory of gravity predicts this, Albert himself didn\'t much care for the idea, at least at first). After about seventy years -- it was discovered in 1929 -- this expansion was kind of old hat, but then new observations came around that shattered the old complacency. The old idea was that the Universe was expanding, but slowing down as it went -- since gravity, as far as anyone knew, could only cause attractive forces. What the new observations demonstrated is that the Universe\'s expansion is, in fact, accelerating -- getting faster with time. This is so shocking that most astronomers and cosmologists couldn\'t believe it at first, and some still don\'t. In this talk, I\'ll explain a bit about how we know this, why it\'s so shocking, and tell you something about the crazy ideas people at Perimeter have for what\'s going on.

One simple way to think about physics is in terms of information. We gain information about physical systems by observing them, and with luck this data allows us to predict what they will do next. Quantum mechanics doesn't just change the rules about how physical objects behave - it changes the rules about how information behaves. In this talk we explore what quantum information is, and how strangely it differs from our intuitions. In particular we see how information about quantum particles can become entangled, leading to seemingly impossibly coordinated behaviour for separate objects, and to phenomena such as quantum teleportation.

A “derivation” of the Schrodinger wave equation based on simple calculus.
Learning Outcomes:
• How to express the de Broglie wave of a free particle, i.e. a complex traveling wave, in terms of the particle’s energy and momentum, and how to differentiate this wave with respect to its space and time variables (x and t).
• How to combine the above mathematical results with the Newtonian expression for the total energy of a particle to get Schrodinger’s wave equation.
• Dirac’s extension of these ideas to Einstein’s expression for the total energy of a particle: introduction to spin, antimatter, and the Standard Model of particle physics.