This year’s session of the big conference on quantum computation, quantum cryptography, and so on is being held in Singapore this year:
• QIP 2011, the 14th Workshop on Quantum Information Processing, 8-14 January 2011, Singapore.
Because the battery on my laptop is old and not very energetic, and I can’t find any sockets in the huge ballroom where the talks are being delivered, I can’t live-blog the talks. So, my reports here will be quite incomplete.
Here are microscopic summaries of just three talks from Monday’s session. You can see arXiv references, slides, and videos of the talks here. I’ll just give links to the slides.
Christian Kurtsiefer gave a nice talk on how to exploit the physics of photodetectors to attack quantum key distribution systems! By cutting the optical fiber and shining a lot of light down both directions, evil Eve can ‘blind’ Alice and Bob’s photodetectors. Then, by shining a quick even brighter pulse of light, she can fool one of their photodetectors into thinking it’s seen a single photon. She can even fool them into thinking they’ve seen a violation of Bell’s inequality, by purely classical means, thanks to the fact that only a small percentage of photons make it down the cable in the first place. Christian and his collaborators have actually done this trick in an experiment here at the CQT!
Tzu-Chieh Wei and Akimasa Miyake gave a two-part joint talk on how the AKLT ground state is universal for measurement-based quantum computation. The AKLT ground state works like this: you’ve got a hexagonal lattice with three spin-1/2 particles at each vertex. Think of each particle as attached to one of the three edges coming out of that vertex. In the ground state, you start by putting the pair of particles at the ends of each edge in the spin-0 (also known as “singlet”, or antisymmetrized) state, and then you project the three particles at each vertex down to the spin-3/2 (completely symmetrized) state. This is indeed the ground state of a cleverly chosen antiferromagnetic Hamiltonian. But has anyone ever prepared this sort of system in the lab?
David Poulin gave a talk on how to efficiently compute time evolution given a time-dependent quantum Hamiltonian. The trickiness arises from Hamiltonians that change very rapidly with time. In a naive evenly spaced discretization of the time-ordered exponential, this would require you to use lots of tiny time steps to get a good approximation. But using a clever randomly chosen discretization you can avoid this problem, at least for uniformly bounded Hamiltonians, those obeying:
for all times . The key is that the high-frequency part of a time-dependent Hamiltonian only couples faraway energy levels, but a uniformly bounded Hamiltonian doesn’t have faraway energy levels.
A couple more things — really just notes to myself:
Steve Flammia told me about this paper relating the Cramer-Rao bound (which involves Fisher information) to the time-energy uncertainty principle:
• Sergio Boixo, Steven T. Flammia, Carlton M. Caves, and J.M. Geremia, Generalized limits for single-parameter quantum estimation.
Markus Müller told me about a paper mentioning relations between Maxwell’s demon and algorithmic entropy. I need to get some references on this work — it might help me make progress on algorithmic thermodynamics. It’s probably one of these:
• Markus Müller, Quantum Kolmogorov complexity and the quantum Turing machine (PhD thesis).
• Markus Müller, On the quantum Kolmogorov complexity of classical strings, Int. J. Quant. Inf. 7 (2009), 701-711.
Hmm — the first one says:
A concrete proposal for an application of quantum Kolmogorov complexity is to analyze a quantum version of the thought experiment of Maxwell’s demon. In one of the versions of this thought experiment, some microscopic device tries to decrease the entropy of some gas in a box, without the expense of energy, by intelligently opening or closing some little door that separates both halves of the box. It is clear that a device like this cannot work as described, since its existence would violate the second law of thermodynamics. But then, the question is what prevents such a little device (or “demon”) from operating.
Roughly, the answer is that the demon has to make observations to decide whether to close or open the door, and these observations accumulate information. From time to time, the demon must erase this additional information, which is only possible at the expense of energy, due to Landauer’s principle. In Li and Vitanyi’s book An Introduction to Kolmogorov Complexity and Its Applications, this cost of energy is analyzed under very weak assumptions with the help of Kolmogorov complexity. Basically, the energy that the demon can extract from the gas is limited by the difference of the entropy of the gas, plus the difference of the Kolmogorov complexity of the demon’s memory before and after the demon’s actions. The power of this analysis is that it even encloses the case that the demon has a computer to do clever calculations, e.g. to compress the accumulated information before erasing it.
So, I guess I need to reread Li and Vitanyi’s book!