C4QEC – CFT PAN – Centrum Fizyki Teoretycznej Polskiej Akademii Nauk

From Fermionic Magic Resources to the Matchgate Commutant and Back

cft — Fri, 15 May 2026 06:18:47 +0000

Abstract:
Understanding the computational complexity of quantum states is a
central challenge in quantum many-body physics. Fermionic Gaussian
states, in particular, can be efficiently simulated on classical
computers and therefore provide a natural baseline against which
genuinely quantum complexity can be assessed. I will briefly introduce
the idea of magic state resource theories, and then focus on a
framework for quantifying fermionic magic resources, also known as
fermionic non-Gaussianity. I will introduce fermionic antiflatness
(FAF) [1], an efficiently computable and experimentally accessible
measure of non-Gaussianity with a clear physical interpretation in
terms of Majorana fermion correlation functions, and briefly discuss
its phenomenology in many-body systems [2]. I will then argue that FAF
naturally leads to questions about the matchgate commutant, namely the
space of operators on k replicas that are invariant under the diagonal
action of the matchgate ensemble. I will discuss how to construct an
explicit orthonormal basis of the matchgate commutant for arbitrary
replica number and system size [3]. Finally, I will describe how this
commutant structure can be used to investigate the formation of
unitary designs in doped matchgate circuits [4].

[1] PS, P. Stornati, X. Turkeshi, PRX Quantum 7, 010302 (2026)
[2] P. R. N. Falcão, J. Zakrzewski, PS, arXiv:2602.00245
[3] PS, X. Turkeshi, P. S. Tarabunga, arXiv:2603.12392
[4] F. B. Trigueros, Z.-H. Sun, X. Turkeshi, PS, P. S. Tarabunga, in preparation

Date: May 20, 2026 2 PM CET
Location: Al. Lotników, room D, ground floor

Remote guests are invited via Zoom:
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Meeting ID: 842 4891 1743
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Semiclassical approximation in representation theory and quantum

cft — Wed, 06 May 2026 09:36:44 +0000

Abstract:
I will give a basic introduction to semiclassical analysis of operators on large representations of unitary groups (or other compact Lie groups). One application of these techniques that may be of interest in quantum information theory is the estimation of von Neumann entropies of density matrices or minimal output entropies of equivariant quantum channels. If time permits, I will briefly explain the relation to the Wehrl conjecture (and its generalizations).

Remote guests are invited via Zoom:
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Meeting ID: 842 4891 1743
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Generalization of Gisin’s Theorem to Quantum Fields

cft — Thu, 23 Apr 2026 06:59:22 +0000

Abstract:

We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields, extending the theorem to cover also states with undefined particle number.

We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser-Horne inequality.

In order to construct the observables leading to a violation, in the first step we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators.

In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space, and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration.

Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the Clauser-Horne inequality.

We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions.

Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.

Remote guests are invited via Zoom:
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Meeting ID: 842 4891 1743
Passcode: 394021

Quantum Statistics in the Minimal Bell Scenario

cft — Tue, 07 Apr 2026 06:25:38 +0000

Abstract:

In any experimental setting, quantum physics provides the statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory and captures some of its core properties. So far, only partial explicit descriptions of this set have been found for Bell-type settings in which entangled states can be shared and measured by independent observers.

Here we obtain the complete explicit and analytical description of a full set of quantum statistics in terms of its extremal points. This is made possible by finding all bipartite quantum states and pairs of binary measurements that can be self-tested, that is, reconstructed from empirical statistics only. Our description precisely reveals some of the extent and limitations of quantum theory.

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Zoom link:
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Meeting ID: 842 4891 1743
Passcode: 394021

Approximation Algorithms and Graph Theory for the Heisenberg Hamiltonian

cft — Fri, 20 Mar 2026 08:38:42 +0000

Abstract:
The Heisenberg Hamiltonian is central for describing quantum magnetism. Here we discuss upper bounds on the ground state energy
that come with an approximation ratio: a guarantee on how close the approximation is to the true ground state energy. One is based on
semidefinite programming, and the second is based on graph theory, and both are highly scalable. References: arXiv:2411.04120,
arXiv:2512.20326.

Remote guests are invited via Zoom:
Zoom link: https://us06web.zoom.us/j/84248911743?pwd=ZsiAOQbRgYCm5IFsArOnb18Fj5IsZh.1
Meeting ID: 842 4891 1743
Passcode: 394021

Date: Mar 11, 2026 02.00 PM CET, Room D