Session P5: Quantum Information Meets Gravitation

Quantum Computational Complexity in the Presence of Closed Timelike Curves

What are the consequences of modifying the laws of physics for the theory of computation? Considering this question in the context of quantum theory has led to a seemingly new class of computing devices known as quantum computers. In this talk I will discuss how modifying computation (in a quantum or classical context) to allow for closed timelike curves leads to a new model of computation. In particular I will discuss how such a model of computation with closed timlike curves can be formulated, whether it can be made robust to noise, and how recent results of Aaronson and Watrous show that this model is nothing more than the well studied complexity class PSPACE. Consequences of these results on foundational issues in quantum theory will also be discussed.   

Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis. This is joint work with Patrick Hayden.   

Entanglement in non-inertial frames and curved spacetime

The insight that the world is fundamentally quantum mechanical inspired the development of quantum information theory. However, the world is not only quantum but also relativistic, and indeed many implementations of quantum information tasks involve truly relativistic systems. In this talk I consider relativistic effects on entanglement in flat and curved spacetimes. I will emphasize the qualitative differences to a non-relativistic treatment, and demonstrate that a thorough understanding of quantum information theory requires taking relativity into account. The exploitation of such relativistic effects will likely play an increasing role in the future development of quantum information theory. The relevance of these results extends beyond pure quantum information theory, and applications to foundational questions in cosmology and black hole physics will be presented.   

Spin-induced non-geodesic motion, Wigner rotation and EPR correlations of massive spin-1/2 particles in a gravitational field

We investigate in a covariant manner, the spin-induced non-geodesic motion of massive spin-1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in an arbitrary curved spacetime, we compute the $O\left( \hbar \right)$ correction to the Wigner rotation of the spin-1/2 particle, whose$O\left( 1 \right)$ contribution is zero on timelike geodesics. We consider specific examples in the Schwarzschild metric for motions in the equatorial plane for (i) particles falling in from spatial infinity with non-zero angular momentum and (ii) circular geodesic orbits. For the latter case we consider the Bell inequalities for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular geodesic in opposite directions.   

Quantum Graphity: a model of emergent locality

Quantum graphity is a background independent condensed matter model for emergent locality, spatial geometry and matter in quantum gravity. The states of the system are given by bosonic degrees of freedom on a dynamical graph on N vertices (that is, changing in time). At high energy, the graph is the complete graph on N vertices and the physics is invariant under the full symmetric group acting on the vertices and highly non-local. We find evidence that the model has a phase, in which the ground state breaks the permutation symmetry to translations and discrete rotations. In this phase the system is ordered, low-dimensional and local. Consideration of the free energy associated with the dominant terms in the dynamics shows that the ground state is thermodynamically stable under local perturbations. The model gives rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. We will reformulate the model in graph-theoretic terms and compare its dynamics to some common graph processes.