Gaussian states, partner modes and an entanglement duality

Abstract: Gaussian states appear everywhere in quantum physics - from condensed matter, to quantum optics and quantum field theory in curved spacetimes. In this talk I aim for three objectives related to Gaussian states:

First, I discuss their partner mode entanglement structure which is well known, but maybe not widely known. This is the fact that a pure Gaussian state under any bipartition decomposes into a sum of two-mode squeezed states, for example, in the Unruh effect or in Einstein-Bose condensates.

Second, I review the powerful Kähler structure formalism for Gaussian states. It captures the geometry of Gaussian states, it is very practical for applications, and it treats both bosons and fermions simultaneously.

Third, to showcase an example connecting bosonic and fermionic systems, I will present an entanglement duality which arises in supersymmetric Gaussian states [1]. Here, bosonic and fermionic partner subsystems, canonically identified by the supercharge construction, exhibit an intriguing duality of their entanglement spectra.

(Time permitting, as a special application, we consider topological insulators and superconductors and their SUSY partners, discussing the recently derived classification of supercharges in this context [2].)

[1] Jonsson, Robert H., Lucas Hackl, and Krishanu Roychowdhury. “Entanglement Dualities in Supersymmetry.” Physical Review Research 3, no. 2 (June 16, 2021): 023213.

[2] Gong, Zongping, Robert H. Jonsson, and Daniel Malz. “Supersymmetric Free Fermions and Bosons: Locality, Symmetry, and Topology.” Physical Review B 105, no. 8 (February 24, 2022): 085423.

HEP - theorymathematical physicsquantum physics

Audience: researchers in the discipline

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Tricontinental Quantum Fundamentals Seminar

Series comments: The Tricontinental Quantum Fundamentals Seminar (3C-QFS) is an online seminar series connecting researchers from Australia, Europe, and America. Our goal is to facilitate discussion between the three continents and bring together those working on foundational topics in relativistic quantum physics, covering but not limited to:

• Measurement, localisation, and causality in relativistic quantum theory
• Energy conditions and quantum inequalities
• Non-locality and observer-dependence of entanglement
• Quantum reference frames and symmetries in quantum theory
• Holography, AdS/CFT, and analogue gravity

For 3C-QFS, we wish to foster an inclusive community and promote open discussion by encouraging a casual atmosphere during the seminars.

The seminars are held online via Zoom, consisting of 40-60 minute talks followed by additional time for questions. We meet every three weeks on Tuesday, alternating between two times in order to connect research communities across two of the three continents.

For those unable to join the seminars live, talks are recorded and hosted on the 3C-QFS YouTube channel.

The seminar series is primarily for students and academics active in the foundations of physics. To sign up for the mailing list and join the seminars live, please complete the registration form on the 3C-QFS website.

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