Speaker: Dominik Šafránek (Institute for Basic Science, South Korea)
Abstract
I will introduce a protocol which allows to unitarily extract work out of sources of quantum states characterized only by a single type of coarse measurement. This defines a new notion of extractable work, which we call observational ergotropy, because it is directly related to observational entropy.
Uncertainty bounds
Date: Monday, April 17, 2023
Time: 14:15
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
Abstract
I will review different kind of uncertainty relations and their
significance in Quantum Information, e.g. for entanglement
and non-locality characterization. Then I will explain how to
obtain (theoretically tight) bounds for these relations using the framework of state polynomial optimization.
A Pub-chat or How we could stop worrying and love Quantum
Abstract
Composing elementary physical systems is one of the most sober and important affairs in the foundations of science, art and every other meaningful endeavours of life. Of course quantum formalism provides us with a recipe for composing multipartite systems. But we would like to explore the ‘what if’ proposals (however wild those may sound) regarding composition of two elementary quantum systems. By the end of the talk I might be able to convince you (via thought experiments) that some of the proposals or ‘possibilities’ are indeed ‘unphysical’. I hope this process may help to ameliorate our affinity towards quantum mechanics.
Reference:
Composition of Multipartite Quantum Systems: Perspective from Timelike Paradigm; Naik et al. Phys. Rev. Lett. 128, 140401 (2021).
Timelike correlations and quantum tensor product structure; Sen et al. Phys. Rev. A 106, 062406 (2022).
Principle of Information Causality Rationalizes Quantum Composition; Patra et al. Phys. Rev. Lett. 130, 110202 (2023).
A tale of unexpected consequences: From foundational problems to mathematical results and applications in quantum information
Date: Wednesday, April 12, 2023
Time: 14:30
Host: Quantum Information and Quantum Computing Working Group, Meeting ID: 844 2780 6931
Abstract
This talk begins with the problem whether entanglement exists in all non-classical operational theories. This problem was already considered as a mathematical problem by George Barker in the 70′ in the context of ordered vector spaces; here we discuss some aspects of the proof that entanglement is a generic feature of non-classical theories. As a consequence of this result, the need for mathematical tools to detect entanglement in all operational theories arises, we address this issue by presenting a generalization of the Doherty-Parrilo-Spedalieri (DPS) hierarchy to operational theories and we also mention the cases when such hierarchy is finite. Finally we discuss the unexpected applications of these results to solve current problems in quantum information, we mainly focus on the problem of semi-device independent certification of Schmidt number of quantum states, for which we derive tight SDP hierarchy.
Generation, storage, and validation of metrologically useful many-body entangled states in the analog and digital quantum simulators in the NISQ era
Speaker: Dr Marcin Płodzień (ICFO – The Institute of Photonic Sciences)
Abstract
Because of challenges in fault-tolerant quantum computing, the main goal for quantum technologies in the next decade is to generate, characterize, and validate massively correlated quantum states. Non-classical correlations, namely entanglement and Bell correlations, are fundamental properties of the quantum many-body systems and crucial resources for emerging quantum technologies. To fully exploit many-body Bell correlations, we need an experimental protocol to generate such quantum states and a method for classifying the depth of many-body Bell correlations.
This talk will discuss our recently proposed protocols for generating and classifying metrologically useful many-body entangled and many-body Bell correlated states in the quantum simulators based on the ultra-cold quantum gases in the optical lattices. Next, we will discuss perspectives of using hybrid quantum-classical machine learning techniques to generate such many-body Bell correlated states on the parametrized quantum circuits in the Noisy Intermediate-Scale Quantum devices.
Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
Date: Wednesday, April 5, 2023
Time: 14:30
Host: Quantum Information and Quantum Computing Working Group, Meeting ID: 844 2780 6931
Speaker: Ravi Kunjwal (Centre for Quantum Information and Communication (QuIC) of the Université libre de Bruxelles (ULB), Brussels, Belgium)
Abstract
The fact that quantum theory radically departs from ‘classical lines of thought’ is a critical driver for its applications in quantum information and computation. A famous example of this radical departure—this nonclassicality—is entanglement. Bell’s theorem shows that shared entanglement can be used to generate correlations between non-communicating parties in ways that are impossible to do without communication if one only had access to classical shared randomness. In their very formulation, both entanglement and Bell’s theorem are composite notions of nonclassicality, i.e., they require at least two parties to be meaningful. Another key notion of nonclassicality is contextuality that follows from the Kochen-Specker theorem: this notion is applicable to single systems. I will present some recent results on the interplay between contextuality and entanglement in composite systems and their consequences for our understanding of restricted models of multiqubit quantum computation with state injection that have been previously proposed. Based on V.J. Wright and R. Kunjwal, Quantum 7, 900 (2023).
Speaker: Jan Głowacki (Center for Theoretical Physics, PAS)
Abstract
I will advertise a way to think about intersecting principles of relativity with the operational approach to quantum physics building on the ideas of the quantum reference frames program. After briefly explaining the need for alternatives/extensions/clarifications of the QFT formalism, I will start with a conceptual discussion of the ideas of relationality and operationality. Then I will present an overview of an approach that puts together these principles in the context of quantum physics, which is the focus of my PhD dissertation. The presentation will necessarily become a bit technical as we go – the framework we are developing with my collaborators is based on covariant positive operator-valued measures, a kind of infinite-dimensional integration, and touches upon the general setup of convex theory in Banach spaces – but I will focus on the bird-eye perspective, without going into technicalities more than strictly necessary (unless such questions arise).
A paper containing most of the results and ideas I will be talking about is now online:
Titouan Carette, Jan Głowacki, Leon Loveridge. “Operational Quantum Reference Frame Transformations”. https://arxiv.org/abs/2303.14002.
Dynamical monitoring in higher dimensions and the emergence of physical realism
Abstract
To better understand the emergence of physical reality in quantum systems during the measurement procedure, we need a model that can interpolate between weak measurements and strong (projective) measurements in systems of any dimension. Although the quantum logic gates to perform that on qubits are known [e.g., A. Touil et al., PRL 128, 010401 (2022)], the question remains open regarding general qudits. Using Heisenberg-Weyl operators, we explicitly find a unitary operator acting on qudits that can be adjusted to interpolate between weak and strong (projective) non-selective measurement regimes, resulting in the monitoring map [P. Dieguez et al., PRA 97, 022107 (2018)]. Surprisingly, within our model, we found out that to get complete information of a higher dimensional system (dimension >= 5), it is not sufficient to interact it with only one qudit of the same dimension. It is necessary to employ a bigger environment to obtain a strong regime. On the other side, weak non-selective measurements can be done with a smaller environment for any dimension. We hope that our research furnishes tools for developments in the foundations of quantum mechanics, but also in quantum metrology.
Reconstruction of global distributions from marginal ones with quantum computers
Date: Monday, March 27, 2023
Time: 14:15
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
Speaker: Eric Aurell (KTH Royal Institute of Technology)
Abstract
Standard quantum-mechanical time inversion is an anti-unitary operation representing time-reversal symmetry. A unitary quantum map hence is hence changed from $\Phi: \rho\to U\rho U^{\dagger}$ to $\Phi^{SQTI}: \rho\to U^{\dagger}\rho U$. One can ask what would be the corresponding operation acting on any CPTP map, which would still give the standard result for unitary maps. The time reversed quantum map $\Phi^R$ must then also be a CPTP map, and the time reversal operation $R$ must be an involution, i.e. $\left(\Phi^R\right)^R=\Phi$. Further, the standard result means $\left(U \cdot U^{\dagger}\right)^R=\left(U^{\dagger} \cdot U\right)$. One class of $R$s fulfilling these natural requirements is standard quantum mechanical time inversion of a system and an environment. This is however contingent on the environmental representation, and is not defined in terms of only the CPTP map itself.
In this talk I consider if $R$ can act linearly. I will give two arguments why this is probably impossible. The first is based on a theorem presented in a recent paper with Chiribella and Zyczkowski, where we considered the analogous question for quantum operations (completely positive trace-non-increasing maps). In this setting one can extend Wigner’s theorem from quantum states to quantum evolutions, such that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary, and this rules out standard quantum-mechanical time inversion. The second argument is based on the fact that a linear involution on the set of all CPTP maps can be lifted to a reflection symmetry in the linear space of trace-preserving maps. If there is an $R$ acting as a linear involution of all CPTP maps, this non-convex set hence must have a nontrivial reflection symmetry, which seems unlikely.
The talk is partly based on joint work with Giulio Chiribella and Karol Życzkowski, published as Phys. Rev. Research 3, 033028 (2021). If time allows I will discuss the possible implications of the above results and conjectures in the light of recent theories of Brukner, Hardy and others.
