Quantum Foundations

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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Local tomography (or tomographic locality) is the principle that the state of a composite systems is determined by the probabilities it assigns to outcomes of experiments performed separately on the component systems. It's well known that complex quantum theory enjoys, and real quantum theory lacks, this feature. This means that a composite of two real quantum systems has additional "global" degrees of freedom. What if we could simply factor these out? In this talk, I'll describe how this can be done, not only for real quantum theory, but for essentially any probabilistic theory. The result is a locally tomographic theory we call the "locally tomographic shadow" of the original. I will also discuss what this shadow theory looks like in the case of real quantum theory. (This is joint work with Howard Barnum and Matthew Graydon).

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In this talk, I will argue and practically illustrate that insights in quantum information, concretely coming from the tensor network representations of quantum many-body states, can help in devising better privacy-preserving machine learning algorithms. In the first part, I will show that standard neural networks are vulnerable to a type of privacy leak that involves global properties of the data used for training, thus being a priori resistant to standard protection mechanisms. In the second, I will show that tensor networks, when used as machine learning architectures, are invulnerable to this vulnerability. The proof of the resilience is based on the existence of canonical forms for such architectures. Given the growing expertise in training tensor networks and the recent interest in tensor-based reformulations of popular machine learning architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed when using machine learning on sensitive data.

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Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using associative information: maximize expected utility. There is an ongoing debate around the origin of probabilities involved in such calculation. In this work, we will show how the probabilities for decision-making can be grounded in causal models by considering decision problems in which the available actions and consequences are causally connected. In this setting, actions are regarded as an intervention over a causal model. Then, we extend a previous causal decision-making result, which relies on a known causal model, to the case in which the causal mechanism that controls some environment is unknown to a rational decision-maker. In this way, action-outcome probabilities can be grounded in causal models in known and unknown cases. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which the players of a strategic game consider causal information.

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