Talks

In this talk, I will consider the centralizer of the quantum group U_q(sl_2) in the tensor product of three identical spin representations. The case of spin 1/2 (fundamental representation) is understood within the framework of the Schur-Weyl duality for U_q(sl_N), and the centralizer is known to be isomorphic to a Temperley-Lieb algebra. The case of spin 1 has also been studied and corresponds to the Birman-Murakami-Wenzl algebra. For a general spin, I will explain how to describe explicitly the centralizer (by generators and relations) using a combination of the braid group algebra and the Askey-Wilson algebra, which has been introduced in the context of orthogonal polynomials.

---

Zoom link: https://pitp.zoom.us/j/98471794356?pwd=NjZFdjRFaDFON05HNkdTZS9hZTUvQT09

Tsirelson’s problem involves two agents, Alice and Bob, who apply measurements on the same quantum system, K. It asks whether commutation, i.e., independence of whether Alice or Bob measures first, is sufficient to conclude that Alice and Bob’s measurements can be factorised so that they act non-trivially only on distinct subsystems of K. In this talk, I will present a “fully quantum generalisation” of this problem, where Alice and Bob’s measurements are replaced by operations on K that may depend on additional quantum inputs and produce quantum outputs. As for Tsirelson’s original problem, it turns out that commutation indeed implies factorisation, provided that all relevant systems are finite-dimensional.

This is joint work with Ramona Wolf; preprint available at arXiv:2308.05792.

---

 Zoom link https://pitp.zoom.us/j/99031410183?pwd=MzVoQXpPSll6bFp1b1g3U2J4U21rZz09

Finding ground states of quantum many-body systems is one of the most important---and one of the most notoriously difficult---problems in physics, both in scientific research and in practical applications.  Indeed, we know from a complexity-theoretic perspective that all methods  (quantum or classical) must necessarily fail to find the ground state efficiently in general. The ground state energy problem is already NP-hard even for classical, frustration-free, local Hamiltonians with constant spectral gap. For general quantum Hamiltonians, the problem becomes QMA-hard.

Nonetheless, as ground state problems are of such importance, and classical algorithms are often successful despite the theoretical exponential worst-case complexity, a number of quantum algorithms for the ground state problem have been proposed and studied. From quantum phase estimation-based methods, to adiabatic state preparation, to dissipative state engineering, to the variation quantum eigensolver (VQE), to quantum/probabilistic imaginary-time evolution (QITE/PITE).

Dissipative state engineering was first introduced in 2009 by Verstraete, Cirac and Wolf and by Kraus et al. However, it only works for the restricted class of frustration-free Hamiltonians.

In this talk, I will show how to construct a dissipative state preparation dynamics that provably produces the correct ground state for arbitrary Hamiltonians, including frustrated ones. This leads to a new quantum algorithm for preparing ground states: the Dissipative Quantum Eigensolver (DQE). DQE has a number of interesting advantages over previous ground state preparation algorithms:

• The entire algorithm consists simply of iterating the same set of   simple local measurements repeatedly.
• The expected overlap with the ground state increases monotonically with the length of time this process is allowed to run.
• It converges to the ground state subspace unconditionally, without any assumptions on or prior information about the Hamiltonian (such as spectral gap or ground state energy bound).
• The algorithm does not require any variational optimisation over parameters.
• It is often able to find the ground state in low circuit depth in practice.
• It has a simple implementation on certain types of quantum hardware, in particular photonic quantum computers.
• It is immune to errors in the initial state.
• It is inherently fault-resilient, without incurring any fault-tolerance overhead. I.e.\ not only is it resilient to errors on the quantum state, but also to faulty implementations of the algorithm itself; the overlap of the output with the ground state subspace degrades smoothly with the error rate, independent of the total run-time.

I give a mathematically rigorous analysis of the DQE algorithm and proofs of all the above properties, using non-commutative generalisations of methods from classical probability theory.

---

Zoom link https://pitp.zoom.us/j/96022753460?pwd=SWlUVkVta1RyY3dsWUJWckRqOHdNdz09

We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09

Activation of Bell nonlocality refers to the phenomenon where some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent and semi-device-independent entanglement certification, with a single copy of the state and local measurements. In this talk I will review the state of the art on activation of nonlocality and existence of local hidden variable models, introduce the broadcasting technique and outline several interesting results and research directions.

---

Zoom link  https://pitp.zoom.us/j/91214624839?pwd=dXNUOERLMldScjczemlaSUhFbFNWQT09