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Process matrices are objects that comprehensively describe multipartite quantum processes and their correlations. These matrices simultaneously play the roles of quantum states and quantum channels, and, to ensure a well-defined probability distribution, they are constrained to be positive. A key advantage of the process matrix formalism is that it can be used to describe processes with an indefinite causal order, which obey local quantum mechanics but cannot take place within a global causal structure. In this talk, i will give a complete introduction to the process matrix formalism and share preliminary results about the geometric positivity constraints of a special class of parameterised process matrices.

A fundamental area in statistical analysis is the study of which causal structures connecting the events of interest can explain the correlations that are observed between them. This is done through the falsification of invalid causal models. Our causal structure might posit the existence of hidden (unobserved) causes between the observed events. For example, if we see a positive correlation between the numbers of shark attacks and ice cream sales, we do not expect to explain it by a direct causal influence between these two things; instead, there should be a hidden common cause (for example, the Summer) that explains the correlation. Physicists also have a vested interest in falsifying causal hypotheses involving hidden variables. Bell's Theorem, for example, highlights the failure of many such classical causal hypotheses to explain the correlations predicted by quantum theory. In the scenario which Bell considered, if instead of treating the unobserved causes of classical random variables we treat them as potentially entangled quantum systems, we can explain a strictly larger set of correlations. Out project explores a simple but difficult question: In what other causal structures this also happens? In other words, for a given causal hypothesis, would the set of correlations it can explain expand if we relax our assumptions regarding posited unobservable systems to allow for shared entanglement? By a series of tricks developed during the PSI Winter School, we found that allowing for quantum causes makes an operational difference in a large number of causal hypotheses involving four observed variables. This work is of general interest as it generalizes Bell's Theorem: it exposes (qualitatively novel?!) advantages afforded by quantum theory over classical models. Bell's Theorem has proven crucially insightful in efforts to provide a causal accounting of quantum theory, and has inspired a plethora of quantum information theoretic protocols; similar dividends may be implicitly suggested by this work.

I will discuss a recent result on an intimate link between two a priori distinct phenomena: quantum nonlocality without entanglement and classically-achievable indefinite causal order. The first phenomenon refers to a multipartite scenario where the parties are unable to perfectly discriminate orthogonal product states drawn from an ensemble of quantum states by using local operations and classical communication (LOCC). The second (hypothetical) phenomenon refers to a multipartite scenario where the parties can communicate classically but the local operations of each party are in the future of the other parties, i.e., they cannot be ordered causally. Specifically, I will show how three separated parties with access to a classical process exhibiting indefinite causal order---the AF/BW process---can perfectly discriminate the states in an ensemble---the SHIFT ensemble---that exhibits quantum nonlocality without entanglement. Time permitting, I will discuss the generalization of this result beyond the tripartite case and comment on its connection with separable operations that are outside LOCC. 

 

Based on joint work with Ämin Baumeler, arXiv:2202.00440.

Zoom Link: https://pitp.zoom.us/j/93727212623?pwd=cjVRL3cvMmhicDRic3lXRFBkNi9xZz09

A black hole quantum state (Hartle-Hawking or Boulware)  is usually defined in a fixed background of a classical black hole. In my talk I will discuss the corresponding space-time geometry when the back-reaction is taken into account. The important questions include: does the back-reacted geometry always contain a horizon?; how it depends on the choice of the quantum state?;  and what is the right choice for the quantum state for the non-physical fields such as ghosts? I will answer these and other questions in the context of a two-dimensional dilaton gravity. The talk is based on a joint recent work with D. Sarkar and Y. Potaux, arXiv:2112.03855.

Zoom Link: https://pitp.zoom.us/j/5053597405?pwd=YjU2VVF1L3A1dmR1VWpPMHZFQW9rdz09