Quantum Foundations

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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Information-theoretic insights have proven fruitful in many areas of quantum physics. But can the fundamental dynamics of quantum systems be derived from purely information-theoretic principles, without resorting to Hilbert space structures such as unitary evolution and self-adjoint observables? Here we provide a model where the dynamics originates from a condition of informational non-equilibrium, the deviation of the system’s state from a reference state associated to a field of identically prepared systems. Combining this idea with three basic information-theoretic principles, we derive a notion of energy that captures the main features of energy in quantum theory: it is observable, bounded from below, invariant under time-evolution, in one-to-one correspondence with the generator of the dynamics, and quantitatively related to the speed of state changes. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions, establishing a bridge between dynamical and information-theoretic notions.

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In this talk the role of information theory in the description of physical evolutions will be discussed. After defining information quantifiers, their contractivity with respect to physical dynamics will be explained, a requirement which simply encodes the intuition that noisy transformations should lose information. The interplay between the two concepts will be exemplified for Markovian evolutions, showing how Markovianity can be defined in purely information theoretic terms. Extending on this result, we prove our main theorem: that all physical maps can be defined solely in terms of a particular metric on the space of density matrices, the Fisher information. This result should be understood in the context of reconstruction of quantum mechanics, proving once again the key role of information in shaping our description of the world.

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In the near future, where only a small number of companies and institutions will have access to large-scale quantum computers, it is essential that clients are able to delegate their computations in a secure way, without their data being accessible by the server. The field of blind quantum computation has emerged in recent years to address this issue, however, the majority of work on this topic has so far been restricted to the secure computation of sequences of quantum gates acting on a quantum state. Yet, a client capable of performing quantum subroutines may want to conceal not only their quantum states but also the subroutines they perform themselves. In this work, we introduce a framework of higher-order blind quantum computation, where a client performs a quantum subroutine (for example a unitary gate), which is transformed in a functional way by a server with more powerful quantum capabilities (described by a higher-order transformation), without the server learning about the details of the subroutine performed. As an example, we show how the DQC1 algorithm for estimating the trace of a unitary gate can be implemented securely by a server given only an (extended) black-box description of the unitary gate. Finally, we extend the framework to the case where the details of the server's algorithm are also concealed from the client.

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What is a measurement? This, it turns out, is the most difficult question in physics today. In this talk, I will explain why the measurement problem is important and why all attempts to solve it so far have failed. I will then discuss the obvious solution to the problem that was, unfortunately, discarded half a century ago without ever being seriously considered: Superdeterminism. After addressing some common objections to this idea, I will summarize the existing approaches to develop a theory for it.

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