Quantum Foundations

What does it mean for quantum state to be genuinely fully multipartite? Some would say, whenever the state cannot be decomposed as a mixture of states each of which has no entanglement across some partition. I'll argue that this partition-centric thinking is ill-suited for the task of assessing the connectivity of the network required to realize the state. I'll introduce a network-centric perspective for classifying multipartite entanglement, and it's natural device-independent counterpart, namely a network-centric perspective for classifying multipartite nonclassicality of correlations. Time permitting, we can then explore semidefinite programming (SDP) algorithms for convex optimization over k-partite-entangled states and k-partite-nonlocal correlations relative to the network-centric classification. Joint work with Denis Rosset and others. We will compare the new quantum-inflation techniques to the classical inflation of arXiv:1609.00672. I'll share a few results made possible by these SDPs, while being openly critical about some disappointing apparent limitations.

Violations of Bell inequalities have traditionally been used to refute a local-realistic description of the world. Not surprisingly, under the assumption that the world is quantum, they can be used to certify quantum devices. What is surprising is that in some cases this characterisation turns out to be (almost) complete, i.e.~we can determine (almost) everything about the devices and this phenomenon is known as self-testing of quantum systems. Although the first self- testing results can be traced back to the works of Tsirelson published in the 80's, the topic has remained largely unknown until the seminal work of Mayers and Yao in 1998. It has received further exposure with the advent of device-independent quantum cryptography to which it is closely connected. In this talk I will give a brief introduction to the topic of self-testing and discuss some recent developments, e.g.~robust self-testing, weak self-testing, self-testing of entangled measurements, self-testing of high-dimensional systems or self-testing in prepare-and-measure scenarios.

Studying the usefulness of resources can be formalized via the framework of a resource theory. However, the complete answer to the question whether a certain resource is more useful than another one is often hard to find in many of the numerous applications of the framework. Approximate answers can be found by identifying so-called monotones—measures of "resourcefulness". I will present several generic constructions of monotones, of which many monotones known in the literature are concrete examples of. These constructions provide a way to relate monotones in different resource theories, thus enabling for the translation of results between them.

In general relativity, the picture of space–time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass–energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.

Convex optimization, linear and semidefinite programming in particular, has been a standard tool in quantum information theory, giving certificates of local and quantum correlations, contextuality, and more. Increasingly, similar methods are making headways in quantum many-body physics, giving lower bounds -- and thus certificates -- on the ground state energy. The disadvantage of such methods is that they do not scale well to large system sizes, whether those systems are multiparty Bell scenarios or lattice models of numerous sites. Machine
learning is entering the field as the latest buzzword. While it provides a more scalable alternative to convex programming and enables forming new conjectures, the outcome of learning methods remains uncertified. In this talk, I introduce the most important paradigms in machine learning for quantum information theory, give an overview of some earlier work in the field, argue for the importance of certifiable predictions of learning algorithms, and present some of our preliminary results.

In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? The relational approach to physics suggests that all the features of a system —such as entanglement and superposition— are observer-dependent: what appears classical from our usual laboratory description might appear to be in a superposition, or entangled, from the point of view of such a quantum reference frame. In this work, we develop an operational framework for quantum theory to be applied within quantum reference frames. We find that, when reference frames are treated as quantum degrees of freedom, a more general transformation between reference frames has to be introduced. With this transformation we describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, which we explore in the case of ‘superposition of Galilean translations’ and ‘superposition of Galilean boosts’. In addition, we consider the situation when the reference frame moves in a ‘superposition of accelerations’, which leads us to extend the validity of the weak equivalence principle to quantum reference frames.

There has been a dissatisfaction with the postulates of quantum mechanics essentially since the moment that those postulates were first written down. Over the years since there have therefore been many attempts (some successful and some less so) to reconstruct quantum theory from various sets of postulates. The aim being to gain a deeper understanding of the theory by providing a conceptually clear underpinning from which the standard formalism can be derived. In this talk I present recent work with Carlo Maria Scandolo and Bob Coecke (arXiv:1802.00367) in which we reconstruct quantum theory from purely diagrammatic postulates within the process theory framework, showing that the conceptual bare-bones of quantum theory concerns the manner in which systems and processes compose.

In order to think about the foundations of physics it is important to understand the logical relationships among the physical principles that sustain the building. As part of these axioms of physics there is the core hypothesis that, how the Universe is partitioned into systems and subsystems is a subjective choice of the observer that should not affect the predictions of physics. Other foundational principles are the Postulates of Quantum Mechanics. However, we prove that these are not independent from the “independence of subsystem partitioning” hypothesis described above. In particular, we prove that the mathematical structure of quantum measurements and the formula for assigning outcome probabilities are implied by the mentioned hypothesis and the rest of quantum postulates. 

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this talk, I will relax the assumption that quantum channels are combined classically, and I will show that, in certain situations, combining quantum channels in an indefinite causal order allows us to achieve tasks that are impossible in conventional quantum Shannon theory. Specifically, I will show a phenomenon of causal activation, whereby two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference.

In this talk, I will discuss two important cryptographic tasks in a post-quantum world. I will discuss the impossibility of bit-commitment and the possibility of physically unforgeable money in the framework of Generalized Probabilistic Theories. Our proofs rely crucially on cone programming, a natural generalization of semidefinite programming. This is based on work with John Selby, arXiv:1803.10279 and arXiv:1711.02662.  

The distillation of quantum resources such as entanglement and coherence forms one of the most fundamental protocols in quantum information and is of outstanding operational significance, but it is often characterized in the idealized asymptotic limit where an unbounded number of independent and identically distributed copies of a quantum system are available. Physical considerations necessarily limit the number of copies available as well as restrict our ability to perform coherent state manipulations over a large numbers of systems, which makes it crucial to be able to characterize how well we can distill resources in realistic, non-asymptotic settings.

We introduce a framework for the non-asymptotic characterization of two related operational tasks, the distillation as well as environment-assisted distillation of quantum coherence. We establish a complete description of the achievable rates of distillation in the one-shot setting under several different classes of free operations, which we show to correspond to the optimization of smoothed entropic quantities as semidefinite programs. We introduce a class of coherence measures which quantify the best achievable fidelity of distillation, and use them to obtain an explicit analytical characterization of coherence distillation for all pure states. Further, we provide insight into the distillation of entanglement, revealing new operational similarities and differences between the resource theories of coherence and entanglement.

This talk is based on joint work with Kun Fang, Xin Wang, and Gerardo Adesso (arxiv:1711.10512) as well as with Ludovico Lami and Alexander Streltsov (in preparation).