Talks

The sampling of Markov processes constrained to both initial and final states has been explored theoretically in recent years. In our work, we have devised a novel method to sample such processes, thus translating conceptual results into a practical approach which will find applications in a wide range of disciplines. To illustrate the benefits of our method we sampled trajectories in the Mueller-Brown potential, allowing us to generate transition paths which would otherwise be obtained at a high computational cost with standard Kinetic Monte Carlo methods because commitment to a transition path is essentially a rare event. We then applied our method to a single-cell RNA sequencing dataset of mouse pancreatic cells to investigate the cell differentiation pathways of endocrine-cell precursors. By sampling Markov bridges for a specific differentiation pathway we obtained a time-resolved dynamics that can reveal features such as cell types which behave as bottlenecks. The ensemble of trajectories also gives information about the fluctuations around the most likely path. For example, we quantified the statistical weights of different branches in the differentiation pathway to alpha cells.

In a simple, constant environment does evolution continue forever? Does extensive diversification via small genetic and ecological differences? What are general evolutionary consequences of organismic complexity? Hints from long term laboratory evolution experiments and from genomic data of within-species bacterial diversity motivate considering these questions. Several simple models of evolution with small ecological feedback will be introduced, with the high dimensionality of phenotype space enabling mathematical analysis.

A Bell scenario can be conceptualized as a "communication" scenario with zero rounds of communication between parties, i.e., although each party can receive a system from its environment on which it can implement a measurement, it cannot send out any system to another party. Under this constraint, there is a strict hierarchy of correlation sets, namely, classical, quantum, and non-signalling. However, without any constraints on the number of communication rounds between the parties, they can realize arbitrary correlations by exchanging only classical systems. We consider a multipartite scenario where the parties can engage in at most a single round of communication, i.e., each party is allowed to receive a system once, implement any local intervention on it, and send out the resulting system once. Taking our cue from Bell nonlocality in the "zero rounds" scenario, we propose a notion of nonclassicality---termed antinomicity---for correlations in scenarios with a single round of communication. Similar to the zero rounds case, we establish a strict hierarchy of correlation sets classified by their antinomicity in single-round communication scenarios. Since we do not assume a global causal order between the parties, antinomicity serves as a notion of nonclassicality in the presence of indefinite causal order (as witnessed by causal inequality violations). A key contribution of this work is an explicit antinomicity witness that goes beyond causal inequalities, inspired by a modification of the Guess Your Neighbour's Input (GYNI) game that we term the Guess Your Neighbour's Input or NOT (GYNIN) game. Time permitting, I will speculate on why antinomicity is a strong notion of nonclassicality by interpreting it as an example of fine-tuning in classical models of indefinite causality.This is based on joint work with Ognyan Oreshkov, arXiv:2307.02565.

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Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent studies have shown that quantum measurement itself can induce novel quantum phenomena. One seminal example is a monitored random circuit, which can generate long-range entanglement faster than a random unitary circuit. Inspired by these results, in this talk, we address the following question: When quantum information is encoded in a quantum error-correcting code, how many physical qubits should be randomly measured to destroy the encoded information? We investigate this question for various quantum error-correcting codes and derive the necessary and sufficient conditions for destroying the information through measurements. In particular, we demonstrate that for a large class of quantum error-correcting codes, it is impossible to destroy the encoded information through random single-qubit Pauli measurements when a tiny portion of physical qubits is still unmeasured. Our results not only reveal the extraordinary robustness of quantum codes under measurement decoherence, but also suggest potential applications in quantum information processing tasks.

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In recent years, large galaxy surveys have played a key role in cosmology, drawing together the effort of hundreds of researchers towards a common goal: accurate and precise measurements of the components of the Universe. In this colloquium, I present some details on how these experiments are built and the rich science behind them.  I show the recent cosmological results achieved by the Dark Energy Survey, the Dark Energy Spectroscopic Instrument, and the combination of these experiments with other probes. Finally, I will discuss the new challenges and expected advances by the next generation of surveys