Search Talks

I will rephrase the question, "What is a quantal reality?" as "What is a quantal history?" (the word history having here the same meaning as in the phrase sum-over-histories). The answer I will propose modifies the rules of logical inference in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical logic, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular.

A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information-transmission. Joint work with Robert Koenig.

Quantum random walks have received much interest due to their non- intuitive dynamics, which may hold a key to radically new quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable, readily scalable, and not limited to specific connectivity criteria. In this seminar, I will present an implementation scheme for quantum walking on arbitrarily complex graphs. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient. In addition, by taking advantage of the inherent structure of the CS decomposition of unitary matrices, we are able to implement all coin operations necessary for each step of the walk simultaneously. This scheme can be physically realized using a variety of quantum systems, such as cold atoms trapped inside an optical lattice or electrons inside coupled quantum dots.

Researchers in quantum foundations claim (D'Ariano, Fuchs, ...): Quantum = probability theory + x and hence: x = Quantum - probability theory Guided by the metaphorical analogy: probability theory / x = flesh / bones we introduce a notion of quantum measurement within x, which, when flesing it with Hilbert spaces, provides orthodox quantum mechanical probability calculus.

Entanglement is one of the most fundamental and yet most elusive properties of quantum mechanics. Not only does entanglement play a central role in quantum information science, it also provides an increasingly prominent bridging notion across different subfields of Physics --- including quantum foundations, quantum gravity, quantum statistical mechanics, and beyond. Arguably, the property of a state being entangled or not is by no means unambiguously defined. Rather, it depends strongly on how we decide to regard the whole as composed of its part or, more generally, on the restricted ways in which we are able to observe and control the system at hand. Acknowledging the implications of such an operationally constrained point of view naturally has led to a notion of 'generalized entanglement,' which is directly based on quantum observables and offers added flexibility in a variety of contexts. In this talk, I will survey some of the main accomplishments of the generalized entanglement program to date, with an eye toward recent developments and open problems.

Removing the mystery from quantum mechanics, the Bohmian perspective – a way of describing the motion of quantum particles, and applying this to spacetime singularities (where gravity becomes infinite) like those inside a black hole.

The nature of time, probability and quantum mechanics, philosophy of physics and metaphysics, especially issues involving the role of mathematical tools like symmetry in physics, and applying this formal apparatus to the philosophy of mind.

Black holes are regions of space with gravity so strong that nothing can escape from them, not even light. This isn't science fiction - there's even a gigantic black hole at the center of our galaxy. It's hard to imagine a more effective way to irrevocably erase and destroy a computer's hard drive than to drop it into a nice big black hole. But is the information on that drive really gone forever? Paradoxically, there's a good chance that not only does the information come back, it comes back in the blink of an eye. This surprise return of the information is based on the same principles that might someday make reliable quantum computers a reality. In fact, engineers are already exploiting these principles to help distribute software and stream video over the internet. And that's where the tornadoes come in...

We know the mathematical laws of quantum mechanics, but as yet we are not so sure why those laws should be inevitable. In the simpler but related environment of classical inference, we also know the laws (of probability). With better understanding of quantum mechanics as the eventual goal, Kevin Knuth and I have been probing the foundations of inference. The world we wish to infer is a partially-ordered set ('poset') of states, which may as often supposed be exclusive, but need not be (e.g. A might be a requirement for B). In inference, a state of mind about the world degrades from perfect knowledge through logical OR, which allows for uncertain alternatives. We don't need AND, and we don't need NOT; we just need OR. This display of acceptable states of mind is [close to] a mathematical 'lattice'. We find that the OR structure by itself (!) forces the ordinary rules of probability calculus. No other rules are compatible with the structure of a lattice, so the ordinary rules are inevitable. The standard Shannon information/entropy is likewise inevitable. Taking this idea further, the OR of states of mind gives a lattice of 'Questions' that might be useful for automated learning. Disconcertingly, this lattice is very much larger (in class aleph-2), and the natural valuations on it exhibit large range. I will present this extension, and ask whether we can rationally foresee its use in practical application.