First AGM Meeting on Geometric Quantum Dynamics 2015-2016
16 October 2015, Brunel University
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 David Meier]
Timetable:
10:15 -- 10:45 Coffee
10:45 -- 11:25 Eva-Maria Graefe (Imperial)
11:35 -- 12:15 Esther Bonet-Luz (Surrey)
12:15 -- 13:30 Lunch
13:35 -- 14:15 Dorje Brody (Brunel)
14:25 -- 15:05 Markus Müller (University of Western Ontario)
15:05 -- 15:30 Coffee
15:35 -- 16:15 David Jennings (Imperial)
16:25 -- 17:05 Gerardo Adesso (Nottingham)
The meeting will take place in room 128, John Crank building (more info here)
Titles & abstracts
Gerardo Adesso
Accessible quantification of multiparticle entanglement
We develop analytical results for the computation of a general class of geometric multipartite entanglement measures, defined in terms of any convex and contractive distance from the set of fully separable states, with respect to a chosen partition. For Nqubit mixed states with maximally mixed marginals, our results are exact and provide closed formulas for distancebased entanglement monotones in all possible multipartitions. For an arbitrary mixed state of N qubits, our analysis provides an experimentally friendly lower bound to distancebased multipartite entanglement monotones; evaluation of the bound only requires three local measurements for any N. We demonstrate the usefulness of our approach for the estimation of multipartite entanglement in Nqubit bound entangled states and other states recently implemented in laboratory.
Esther Bonet-Luz
Geometry of Gaussian quantum dynamics
The dynamics of quantum expectation values is considered in a geometric setting, in the particular case of Gaussian states. By restricting to Gaussian states, the dynamics of quantum moments is closed up to second order, coupling the dynamics of expectation values (Ehrenfest equations) to second order moments. Gaussian states are shown to posses a Lie-Poisson structure associated to a semidirect-product group: the Jacobi group. This structure produces new energy-conserving terms in a class of Gaussian moment models (previously appeared in the chemical physics literature) that suffer from lack of energy conservation in the general case. Finally, the ladder operator formulation of these results, involving the complexification of the Lie algebra of the Jacobi group, is shown. For example, this reformulation is particularly convenient for applications in quantum optics, involving coherent squeezed states.
Dorje Brody
Consistency of PT-symmetric Quantum Mechanics
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric—the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.
Eva-Maria Graefe
Wave packet evolution generated by non-Hermitian Hamiltonians in the semiclassical limit
In recent years there has been growing interest in complexified quantum systems described by non-Hermitian Hamiltonians in various fields. Examples are scattering systems and the effective description of absorption and amplification. The classical counterparts of complexified quantum systems, however, remained illusive. In this talk I present some results on the quantum evolution of Gaussian wave packets generated by a non-Hermitian Hamiltonian in the semiclassical limit of small hbar. This yields a generalisation of the Ehrenfest theorem for the dynamics of observable expectation values. The resulting equations of motion for dynamical variables are coupled to an equation of motion for the phase-space metric---a phenomenon having no analogue in Hermitian theories. I will discuss an illustrative example of a non-Hermitian PT-symmetric Harmonic oscillator.
David Jennings
Quantum state spaces and geometric aspects of entanglement
The state space of the simplest possible quantum system (a qubit) is the Bloch sphere, which is simply a solid ball in 3-dimensions. However the state space of the simplest possible bipartite quantum system (2 qubits) is already an intricate 8-dimensional convex body with non-trivial structure. In this talk I shall show that foundational ideas from entanglement provide a way to faithfully represent arbitrary 2-qubit states in 3-dimensions in terms of a “steering ellipsoid” plus local data. This representation permits a geometric analysis of quantum correlations in transparent and intuitive terms. In particular, we find that a quantum state is entangled if and only if its ellipsoid fits inside a tetrahedron which itself fix inside the Bloch sphere. This "nested tetrahedron criterion" leads to a range of applications: it provides a new theorem in classical Euclidean geometry for inscribing solids, a classification for entanglement witnesses and also a novel monogamy of entanglement inequality. Finally, I will discuss higher dimensional generalisations, geometric connections to the theory of quantum phase transitions and some open problems in the area.
Markus Müller
Spacetime and the state space geometry of quantum theory
In 1994, Popescu and Rohrlich asked whether quantum states describe the most general correlations that are consistent with relativity, and answered the question in the negative: there are conceivable correlations ("PR boxes") that satisfy the no-signalling principle, but are stronger than any correlations achievable by quantum states. In this talk, I describe a research program that aims at pursuing this approach much further: it asks in what way the geometry of spacetime and the state space geometry of quantum theory constrain each other. Any answers to this question will have profound implications for our picture of the "architecture of physics", and potentially for the search for a theory of quantum gravity. Concretely, I will first show that relativity of simultaneity constrains the number of degrees of freedom of the quantum bit to either three (which is the correct number), or no more than five (depending on the detailed assumptions). Then I will sketch a route towards understanding the appearance of the Lorentz group in operational terms from quantum communication.
Joint work with Andy Garner, Oscar Dahlsten, and Philipp Hoehn.
Contacts: