# Causality and positivity in causally complex operational probabilistic theories

### APA

Hardy, L. (2023). Causality and positivity in causally complex operational probabilistic theories. Perimeter Institute. https://pirsa.org/23110066

### MLA

Hardy, Lucien. Causality and positivity in causally complex operational probabilistic theories. Perimeter Institute, Nov. 16, 2023, https://pirsa.org/23110066

### BibTex

@misc{ pirsa_PIRSA:23110066, doi = {10.48660/23110066}, url = {https://pirsa.org/23110066}, author = {Hardy, Lucien}, keywords = {Quantum Foundations}, language = {en}, title = {Causality and positivity in causally complex operational probabilistic theories}, publisher = {Perimeter Institute}, year = {2023}, month = {nov}, note = {PIRSA:23110066 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

In the usual operational picture, operations are represented by boxes having inputs and outputs. Further, we usually consider the causally simple case where the inputs are prior to the outputs for each such operation. In this talk (motivated by an attempt to formulate an operational probabilistic field theory) I will consider what I call the "causally complex" situation. Operations are represented by circles. These circles have wires going in and out. Each such wire can represent an input and an output. Further, each operation will have a causal diagram associated with it. The causal structure can be more complicated than the simple case. These circles can be joined together to create new operations. I will discuss conditions on these causally complex operations so that we have positivity (probabilities are non-negative) and causality (to be understood in a time symmetric manner). I will also discuss how these properties compose when we join causally complex operations. Causally complex operations are related to objects in the causaloid formalism as well as to quantum combs.

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Zoom link https://pitp.zoom.us/j/99425886198?pwd=ODR0VVFzQUJHeER4OVJ2cEo3cVdDQT09