Author: dabacon

Seth Lloyd has a new book out Programming the Universe : A Quantum Computer Scientist Takes On the Cosmos . I just picked up a copy and flipped to this amusing anecdote:

…When Shannon showed his new formula for information to the mathematician John von Neumann and asked him what the quantity he had just defined should be called, von Neumann is said to have replied “H.”
“Why H?” asked Shannon.
“Because that’s what Boltzmann called it,” said von Neumann…

That crazy von Neumann.

Congrats to the two winners of the first Best Student Paper Awards for the APS Topical Group on Quantum Information, Concepts and Computation: Michael Garrett (Calgary) and Chris Langer (NIST, Boulder) (What you’ve already seen this announcement, congrats! What you’ve not seen this announcement? Must be because your not a member of the topical group. Maybe you should join? Then again who am I to say what you should do!) The awards are sponsored by the Perimeter Institute (theory) and the Institute for Quantum Computing (experiment) and come with a $500 award, but more importantly with fabulous fame! (Hey no jokes about the “American Physical Society” awards in quantum computing both being sponsered by Canadian institutions.)
Here is the abstract from Michael Garrett’s talk:

9:36AM U40.00007 Stochastic One-Way Quantum Computing with Ultracold Atoms in Optical
Lattices , MICHAEL C. GARRETT, University of Calgary, DAVID L. FEDER, University of Calgary — The one-way model of quantum computation has the advantage over conventional approaches of allowing all entanglement to be prepared in a single initial step prior to any logical operations, generating the so-called cluster state. One of the most promising experimental approaches to the formation of such a highly entangled resource employs a gas of ultracold atoms confined in an optical lattice. Starting with a Mott insulator state of pseudospin-1/2 bosons at unit filling, an Ising-type interaction can be induced by allowing weak nearest-neighbor tunneling, resulting in the formation of a cluster state. An alternate approach is to prepare each spin state in its own sublattice, and induce collisional phase shifts by varying the laser polarizations. In either case, however, there is a systematic phase error which is likely to arise, resulting in the formation of imperfect cluster states. We will present various approaches to one-way quantum computation using imperfect cluster states, and show that the algorithms are necessarily stochastic if the error syndrome is not known.

and here is the abstract from Chris Langer’s talk

8:48AM U40.00003 Robust quantum memory using magnetic-field-independent atomic qubits1, C. LANGER, R. OZERI, J. D. JOST, B. DEMARCO2, A. BEN-KISH3, B. BLAKESTAD, J. BRITTON, J. CHIAVERINI, D. B. HUME, W. M. ITANO, D. LEIBFRIED, R. REICHLE, T. ROSENBAND, P. SCHMIDT, D. J. WINELAND — Scalable quantum information processing requires physical systems capable of reliably storing coherent superpositions for times over which quantum error correction can be implemented. We experimentally demonstrate a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a field B = 0.01194 T. Qubit superpositions are created and analyzed with two-photon stimulated-Raman transitions. We observe the single physical qubit memory coherence time to be greater than 10 seconds, an improvement of approximately five orders of magnitude from previous experiments. The probability of memory error for this qubit during the measurement period (the longest timescale in our system) is approximately 1.4 × 10−5 which is below fault-tolerance threshold for common quantum error correcting codes.

Black holes evaporate via the process of Hawking radiation. If we take the initial pure state describing a body which will collapse and form a black hole which can evaporate, then it would appear that this pure state will evolve, after the complete evaporation, to a state which is mixed. Since it is doing this without leaving any remnant for quantum information to hide in, this would seem to violate the unitarity of quantum theory, which does not allow a closed system pure state to evolve to a closed system mixed state. Similarly, if we consider the an evaporating black hole, there are spacelike surfaces which contain the collapsing body and the outgoing Hawking radiation: therefore if we somehow believe that the outgoing Hawking radiation contains quantum information which we have thrown into the black hole, this process must have cloned this information and thus violated the linearity of quantum theory. This reasoning has been hounding theoretical physicists for ages and is known as the black hole information paradox.
A few years ago, Horowitz and Maldacena proposed a solution to this problem (see hep-th/0310281, “The black hole final state”.) The basic idea of their solution is to use boudary conditions at the black hole singularity to fix this problem. Actually the basic idea of their solution is to use post-selected quantum teleportation. How does this work? Well consider the initial pure state describing the collapsing matter. In addition to this collapsing matter, there will be the Unruh state of the infalling and outgoing Hawking radiation. Now it works out that this Unruh state is basically a maximally entangled quantum state. So what Horowitz and Maldacena propose is that, in order to get the pure state describing the collapsing matter “out” of the black hole, one need only “teleport” this information by using the Unruh radiation. Indeed, we can consider such teleportation: perform a measurement of the pure state describing the collapsing matter and the state of the infalling Hawking radiation in the appropriate (generalized) Bell basis. Now, of course, in order to complete the teleportation procedure we need to send the result of this measurement to the outgoing radiation and apply the appropriate unitary rotation to get the pure state of the collapsing matter outside of the black hole. But, of course, we can’t do this: we can’t send the classical information from inside the black hole to outside. So what Horowitz and Maldacena propose is that instead of performing the full teleportation, a particular result is post-selected for this teleportation. And this result will be the one where you do nothing in the teleportatin protocol. In other words, they postulate that the black-hole singularity acts like a measurement in which one always gets a particular outcome. This is the “final state” projection postulate.
This is a very nice way to try to avoid the black-hole information paradox. One reason is that it seems to put all the craziness at the black-hole singularity, and not of the craziness elsewhere, where we would expect our current ideas about physics to be rather robustly true. But does this really solve the problem? Gottesman and Preskill, in hep-th/0311269 argue that it does not. What Gottesman and Preskill point out is that the collapsing matter and the infalling Unruh radiation will, in general, interact with each other. In this case, the problem is that this interaction can cause the information to no longer be faithfully reproduced outside of the black hole. The problem is that this interaction causes post-selection onto a state which is no longer maximally entangled: the state will then fail at producing the appropriate teleported copy of the state outside of the black hole. Sometimes, in fact, this interaction can completely destroy the effect Horrowitz and Maldacena are attempting to achieve (if we disentangle the post-selected state.) This does not bode well for this post-selected answer to the black-hole information paradox.
So is this the end? Well it is never the end! One might try to show that the amount of information destroyed in the Gottesman-Preskill scheme is small. Now this, in some sense, would be comforting: who would notice a single qubit missing in a world so large? On the other hand, while this might be comforting, it would certainly cause certain consternation among those of us who would like an explanation which is satisfying without giving up even an ounce of information. This question, of the amount of informatin lost, is addressed, in part, in the recent paper “Almost Certain Escape from Black Holes in Final State Projection Models” by Seth Lloyd, Physical Review Letters, 061302 (2006)
Consider the Horowitz and Maldacena scheme as modified by Gottesman and Preskill with an interaction between the infalling and collapsing matter state described by U. Lloyd calculates the fidelity of this scheme, when averaged over all unitaries U according to the Harr measure (this fidelity is the overlap between the initial pure collapsing matter state and the outgoing state after the Horowitz-Maldacena post-selection.) Lloyd finds that this fidelity is 0.85…. In the paper, Seth argues that this is indeed large enough as to indicate that most of the information survives. So, I ask, is 0.85… fidelity really satisfying? I would argue that it is not, even if I accept that averaging over the unitaries makes any sense at all. Why? Well suppose that you daisy chain this procedure. Then it seems that your average fidelity could be as small as desired. Thus while you might argue that there is only a small loss of unitarity for random unitaries, there are physical processes for which this loss of unitarity is huge. This seems to be one of the lessons of quantum theory: destroying only a little bit of information is hard to do without bringing down the whole wagon. Daniel Gottesman says, I think, exactly this in this New Scientist article. Even Lloyd, at the end of his article, hedges his bets a bit:

Final-state projection will have to await experimental and theoretical confirmation before black holes can
be used as quantum computers. It would be premature to jump into a black hole just now.

What about you? Would you jump into a black hole with the fidelity that we could put you back together of 0.85… on average?

I’m visiting the KITP in Santa Barbara because they are having a term long workshop on Topological Phases and Quantum Computation (directed by Sander Bais, Chetan Nayak, and John Preskill.) Unfortunately I won’t be able to stay for the entire workshop. But this isn’t as huge of a blow as it would have been years ago, because, the KITP records all of the talks and puts them online. They can be found here.
Yesterday, T. Sentil gave a talk in which he almost made it through his introduction! Anyway one point which he emphasized is something I have always found fascinating. And that is that topological phases (a loose term which I won’t even try to define) might actually be much more common than is widely thought, but the problem is that we don’t have the tools to see them! From the perspective of quantum error correcting codes, this seems fairly natural. In a quantum error correcting code, local probes without at least a global analysis, can not reveal the information encoded into a quantum error correcting code. Indeed if local probes without global analysis could get at our quantum data, then so too could an environment get to this data. Another way to state this is to say that the order parameter for quantum error correcting codes is a big complicated beast whose measurement cannot be done with the simple tools we currently have in our lab.
As a concrete example of this, consider single-molecule molecules. These are crazy molecules which can achieve permanent magnetization through a single molecule effect (usually at fairly low temperatures.) Basically these molecule have a high spin ground state and a high zero-field splitting such that there is a substantial barrier to leaving the high spin ground state. This effect is the result of a collection of interactions among the lower spin systems. What is interesting is the following observation. Take four spin one-half systems and couple them together anti-ferromagnetically with equal couplings between all four systems (mmm, tetrahedrons.) Such a system will have a spin zero ground state which is two fold degenerate. And this two-fold degenerate ground state is actually a single error quantum error detecting code (see quant-ph/0012018)! But why in the world, if you were a chemist, would you go looking for a spin zero molecule. This is the exact opposite of what you would like to find. Further, you won’t be able to see that there is a quantum error detecting code without a knob which allows you to split the degeneracy of this ground state. And doing this is not a trivial task. In short, exactly since we don’t have the tools to observe this effect, we won’t really be interested in it. You need a crazy theorist to tell you that maybe you should think about trying to engineer such a knob onto your system. What use is a crazy theorist except to tell you crazy stories.
Of course, thinking like this, that there might be hidden orders which we are not smart enough to discover is a good way to make yourself paranoid. What might we be hiding from because our glasses are so opaque? Certainly the role of instrumentation in science is one I find fascinating and, I must admit, a bit scary.