Quantum Information talks

We are pleased to announce that the quantum information theorist Professor Patrick Hayden (Stanford University) will be visiting the Department of Mathematical Sciences next week. Patrick will give a joint NBIA/math-seminar at the NBI in Blegdamsvej on Monday and the Mathematics Colloquium in HCØ on Tuesday.

Quantum information in space and time

Aud A, Niels Bohr Institute, Blegdamsvej Date on Monday, 19th January 2015, 15:15-16:15 (cookies from 14:45 in the NBIA lounge)


What can quantum information theory teach us about spacetime? When it comes to black hole evaporation, quantum cloning and what lies beyond the event horizon, the theory teaches us something we should have already known: that we're confused. But the information theoretic viewpoint can also provide unexpected illumination. This talk will describe two examples of how quantum information theory can reveal unexpected and beautiful structure in spacetime. The first example will address a basic question: where and when can a qubit be? While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. There is a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities. The second example comes from holography. The AdS/CFT correspondence provides a concrete realization of the holographic principle, in which the physics of a “bulk” spacetime volume is completely encoded onto its boundary surface. A dictionary relates the physics of the boundary to the physics of the bulk, but the boundary interpretation of the bulk's extra dimension has always been a bit fuzzy. I'll explain one precise interpretation of that extra dimension, showing how its geometry encodes the entanglement structure of the boundary state.

Quantum Information as Asymptotic Geometry

Aud 4, HCؠon Tuesday, 20th January 2015, 15:15-16:15 (cookies from 14:45 in the math coffee room)


Quantum states are represented as vectors in an inner product space. Because the dimension of that state space grows exponentially with the number of its constituents, quantum information theory is in large part the asymptotic theory of finite dimensional inner product spaces, a field with its own long history. I’ll highlight some examples of how abstract mathematical results from that area, such Dvoretzky’s theorem, manifest themselves in quantum information theory as improvements in quantum teleportation and as the raw material for counterexamples to the field’s famous additivity conjecture. More recently, this perspective has led to methods for encrypting arbitrarily long messages using constant-sized secret keys. In other circumstances, regularity in information being transmitted leads to natural connections with the asymptotic representation theory of the unitary and symmetric groups, the setting for another fruitful ongoing dialogue.