Second AGM Meeting
Second AGM Meeting on Geometric Quantum Dynamics 2017-2018
7 December 2017, Imperial College London
This one-day meeting will cover various disciplines related to geometric quantum dynamics. Specific topics will include geometry of quantum states and reduction by symmetry.
[IMPORTANT! -- All non-speaker attendees are requested to register by writing to Cesare Tronci]
Timetable:
10:00 -- 11:00 Gary Gibbons (Cambridge)
11:00 -- 11:30 Break
11:30 -- 12:30 Sania Jevtic (Imperial)
12.30 -- 14.00 Lunch
14:00 -- 15:00 Michael Foskett (Surrey)
15:00 -- 15:30 Break
15:30 -- 16:30 Dorje Brody (Brunel)
The meeting will take place in room RSM 2.42, Royal School of Mines (more info here)
Titles & abstracts
Dorje Brody
Information loss in phase transitions
There are certain universal features associated with a range of critical phenomena, such as thermal phase transitions or transitions associated with 'exceptional points' where eigenvectors of a matrix coalesce. These include, for example, the breakdown of adiabatic approximations, the curvature divergence of the parameter-space at critical points, or the loss of information concerning the initial state of the system as one passes through critical points. This talk will sketch some of these ideas that suggest that perhaps exceptional point physics is not all that different from critical phenomena in thermal physics.
Michael Foskett
Wavefunction factorizations and gauge structure dynamics in quantum chemistry
The interplay of electronic and nuclear dynamics is an active area of research in quantum chemistry, with many models aiming to capture non-adiabatic effects whilst simplifying the computational task of the quantum many body problem. We consider a geometric approach to the ‘Exact Factorisation’ of the molecular wavefunction and use the technique of Euler-Poincaré reduction to derive a closed system of equations. Interestingly, this approach naturally leads to introducing the dynamics of the Wilczek-Zee gauge connection, a generalisation of the celebrated Berry connection. Similar gauge structures also appear in the gauge theory of defects for elastic media, thereby suggesting that the evolution of the Wilczek-Zee connection can capture the dynamics of singularities such as conical intersections.
Gary Gibbons
Applying null geodesics in a Lorentzian spacetimes to problems unconnected with General Relativity
The problem of finding null geodesics in a stationary spacetime may be reduced to solving a Zermelo problem or a Randers-Finsler problem in a Riemannian manifold and conversely those two problems can be lifted to the null geodesic problem in a stationary spacetime. More generally any natural dynamical problem me be lifted to the null-geodsic flow of a Lorentzian manifold. In my talk I will explain this connection give some recent examples of its use.
Sania Jevtic
Quantum steering with positive operator-valued measures
Quantum steering is one of the three forms of quantum non-locality, the other two being Bell-nonlocality and entanglement. The quantum steering scenario most closely resembles the seminal thought experiment of Einstein, Podolsky, and Rosen (1935). Two distant observers, Alice and Bob, each possess a quantum particle, and these two particles are entangled. Alice can perform measurements on her particle which affect, or “steer”, the state of Bob’s particle. The fascinating aspect of this is that, for certain entangled states of the two particles, Bob’s steered ensembles cannot be described in a classical way, that is, using a model of local hidden states. Such entangled states are called “steerable” (otherwise they are unsteerable).
Steerable states have been verified experimentally and have proven advantageous in a variety of quantum information tasks. Nevertheless, the set of steerable states is still very poorly understood. Methods for checking whether a state is steerable have been presented in cases when Alice’s measurements are restricted, for example, she can only perform projective, or von Neumann, measurements. There are currently no known efficient methods for tackling steerability when she has the ability to perform generalised measurements, known as “positive-operator valued measures” (POVMs).
By viewing the steering as a problem of nested convex objects, we derive an inequality which can help to determine the boundary of steerable vs unsteerable quantum states for all measurements. Given an ansatz u for the "ensemble of local hidden states", we can systematically test whether a given entangled state is unsteerable with respect to u. We test our inequality on a “Werner state” and confirm (numerically to a high precision) a longstanding conjecture that Werner state is unsteerable for all measurements when it is an equal mixture of the maximally mixed state and a singlet. As a novel application, we also test our inequality on states that are mixtures of Bell pairs (“T-states”), and our numerics show that here also steerability for all measurements coincides with steerability for projective measurements.
Contacts: