Hi all,
Tomorrow Sébastien Garmier will tell us about his semester thesis entitled 'The Black Hole Information Loss Paradox in the Context of Analogue Gravity'. See below for the abstract. The talk will take place at 1.30pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
Titel:
The Black Hole Information Loss Paradox in the Context of Analogue Gravity
Abstract:
We investigate the possibility of approaching the black hole information loss paradox from the point of view of analogue gravity models. More generally, we ask whether analogue models can at all make inferences about gravity. To this end we give an introduction to black holes, the black hole information loss paradox, and analogue gravity models, before attempting to formulate the information loss paradox in the context of analogue gravity. We find that crucially, the notion of black hole entropy is missing, placing a discussion of the paradox in that context out of reach. Simultaneously, we argue based on the ubiquity and generality of analogue models, that they are unlikely to possess deep connections with gravity.
Hi all,
Tomorrow Tony Metger will tell us about ‘Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations'. See below for the abstract. The talk will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
Hi all,
Tomorrow our visitor Patrik Potts will tell us about his work on 'Optical coherent feedback control of a mechanical oscillator'. See below for the abstract. The talk will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
Optical coherent feedback control of a mechanical oscillator
We present the theoretical description and experimental realization of an optical coherent feedback platform to control the motional state of a nanomechanical membrane in an optical cavity. The coherent feedback loop consists of a light field interacting twice with a mechanical oscillator in different cavity modes. Tuning the optical phase and delay of the feedback loop allows us to control the motional state of the mechanical oscillator, its frequency shift and damping rate, which we use to cool the membrane close to the ground state. In the optimal cooling conditions, we derive an expression for the minimal number of phonons and show that this new technique enables ground state cooling. Experimentally, we show that we can cool the membrane to a state with 4.89 ± 0.14 phonons (480 μK) in a 20 K environment. This lies below the theoretical limit of dynamical backaction cooling in the unresolved sideband regime. The described feedback scheme is very versatile and could be implemented in various optomechanical systems.
Hi all,
Tomorrow Vilasini will tell us about her work on 'Embedding cyclic causal structures in acyclic spacetimes: no-go results for process matrices'. See below for the abstract. The talk will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Title: Embedding cyclic causal structures in acyclic spacetimes: no-go results for process matrices
V. Vilasini and Renato Renner, based on https://arxiv.org/abs/2203.11245
Abstract: Causality can be defined in terms of a space-time structure or based on information-theoretic structures, which correspond to different notions of causation. The process matrix framework describes quantum indefinite causal structures in the information-theoretic sense, but the physicality of such processes remains an open question. At the same time, there are several experiments in Minkowski spacetime (which gives a definite spacetime notion of causality) that claim to implement indefinite information-theoretic causal structures, suggesting an apparent tension between these notions. To address this, we develop a general framework that disentangles these two notions and characterises their relationship in scenarios where quantum systems are not necessarily localised in spacetime. Formulating (possibly cyclic) quantum causal structures in terms of a composition of quantum maps through feedback loops, we proceed to describe their embedding in acyclic background spacetimes. Then relativistic causality takes the form of a compatibility condition between the information-theoretic and spacetime causal order relations. Connecting the process matrix formalism to cyclic causal structures with a focus on causal relations that can be inferred operationally through agents’ interventions, we derive a number of no-go results for physical realisations of process matrices in a spacetime. In particular, this reveals that it is impossible to physically realise indefinite causal order processes with spacetime localised systems. Further, we show that any realisation of an indefinite causal order process respecting relativistic causality in a background spacetime ultimately admits a fine-grained description in terms of a definite acyclic information-theoretic causal structure that is consistent with the light-cone structure of the spacetime. This resolves the apparent tension between the two causality notions. Finally, we discuss the operational meaning of indefinite causal structures in light of our results.
Hi all,
Tomorrow Lukas Brenner will tell us about their Semesterthesis with Philipp Kammerlander entitled 'Comparing Entropies via Erasure Processes on Multiple-Conserved-Quantity-Memories'. See below for the abstract. The talk will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Abstract:
The relevance of memories in the context of thermodynamics was illustrated by their appearance in Szilard’s engine as a solution to Maxwell’s demon paradox. We formulize the notion of memories in the language of the Kammerlander framework, which provides the possibility to talk about thermodynamics of single and multiple conserved quantities. Memories are introduced as a family of thermodynamic systems which allow for generalized erasure processes i.e. resetting a memory to a reference state is achievable outside the realm of energy conservation. Such processes can be exploited in order to compare entropies induced by different conserved quantities. We demonstrate that a universal ratio of entropies is established when relating optimal erasure processes of memories.
Hi all,
Tomorrow our visitor Michèle Wigger will tell us about "Strong and $\epsilon$-Dependent Converses for Classical Coding and Hypothesis Testing Problems". See below for the abstract. The talk will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Title: "Strong and $\epsilon$-Dependent Converses for Classical Coding and Hypothesis Testing Problems"
Abstract:
This is a classical talk, where I will be presenting new simple strong converse proofs for basic classical source coding and hypothesis testing problems, and if time permits also for classical channel coding. For the basic source and channel coding setups, the proofs only use a change of measure argument on the strongly typical set and the asymptotic analysis of the new measure. This proof method is also extended to a source coding setup under relaxed expected rate constraints, in which case the minimum compression rate depends on the allowed probability of error $\epsilon$ and an $\epsilon$-dependent converse is required. In the second part of the talk we present converse proof methods for hypothesis testing setups, where the change of measure argument is not sufficient, but has to be completed with proofs of asymptotic Markov Chains. We again also consider expected resource or secrecy constraints and provide probability-of-error-dependent converse proofs under these expected constraints.
Hi all,
Tomorrow we will have two talks:
Eliott Mamon will tell us about 'How to model quantum bomb-testing? A framework for “interaction-free” experiments'.
Alexander Schmidhuber will talk about 'Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis'.
See below for the abstracts. The talks will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best,
Ladina
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Title:
How to model quantum bomb-testing? A framework for “interaction-free” experiments
Abstract:
Taking inspiration from the "counterfactual computation" framework of [1], an axiomatic framework for studying quantum experiments that can lead to counterfactual outcomes, and more generally, interaction-free outcomes, is proposed. It is based on a separation of the Hilbert space into "off" and "on" subspaces. To both motivate the framework itself and better understand what devices one should actually choose in it to model a given experimental setup, we start by introducing a purely classical "interaction-free" framework (in which counterfactual outcomes are impossible by construction). There, one makes a conceptually simpler ansatz of such a classical framework instance, and then, applies a quantum extension scheme, wherein several "choices of coherence" are left to be made --- first within off-states and on-states, and then between the two. We highlight a resulting feature of the framework: if a lack of coherence between off-states and on-states is chosen in the extension scheme for a particular device, then the resulting quantum setup cannot yield counterfactual outcomes for the other devices.
We apply our framework to approach modeling quantum "bomb-testing" experiments, illustrating how the framework structures the different candidate models together. We also discuss how the framework deals with modeling "quantum Zeno effect" type bomb-testing protocols like the Kwiat et al. protocol of [2]. Notably, we underline how the usual notion of "interaction-free" on them is recovered within our framework.
Lastly, we consider formalizing an "existence of noncontextual model" question for a given protocol of our framework. We then numerically, using the unit separability criterion of [3], assess this question in the negative for the Kwiat et al. N insertion protocol, for N = 4,...,8.
[1] Graeme Mitchison and Richard Jozsa. "Counterfactual computation". Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457.2009 (2001), pp. 1175–1193.
[2] Paul Kwiat et al. “Interaction-free measurement”. Physical Review Letters 74.24(1995), pp. 4763–4766.
[3] Victor Gitton and Mischa P. Woods. "Solvable criterion for the contextuality of any prepare-and-measure scenario". Quantum 6 (2022), p. 732.
Title:
Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis (https://arxiv.org/abs/2209.14286)
Abstract:
Quantum algorithms for topological data analysis (TDA) have received a surge of attention recently. They seem to provide an exponential advantage over the best classical approach while remaining immune to dequantization procedures and the data-loading problem. In this talk, I will argue that quantum algorithms for TDA run in exponential time for almost all inputs by showing that the central problem of TDA - estimating Betti numbers - is intractable even for quantum computers. Specifically, we prove that the problem of computing Betti numbers exactly is #P-hard, while the problem of approximating Betti numbers up to multiplicative error is NP-hard. Because quantum computers are not expected to solve #P-hard or NP-hard problems in sub-exponential time, our results imply that quantum algorithms for TDA only provide a polynomial advantage. We verify our claim by showing that the seminal quantum algorithm for TDA developed by Lloyd et al. achieves a quadratic speedup over the best classical approach in almost all cases. Finally, we argue that an exponential quantum advantage can be recovered if problems beyond TDA are considered.