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Quantum Causal Unravelling

Ge Bai (presenting, HKU), Ya-Dong Wu (HKU), Yan Zhu (HKU), Masahito Hayashi (SUSTech), Giulio Chiribella (HKU)

arXiv:2109.13166

Quantum Information�& Computation Initiative

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Quantum Causal Unravelling

Many natural processes arise from a sequence of basic interactions, but we may not have access to individual events

E.g., scattering experiments in high energy physics

Quantum causal unravelling determines:
whether the process can be broken down into a sequence of simpler interactions
the order of such interactions
which systems take part in each interaction

by accessing only the inputs and outputs of the process (black-box access)

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Quantum Causal Unravelling

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Given: a process consisting of a sequence of interactions, each involving a subset of the inputs/outputs

Objective: infer the causal structure of the interactions solely from the input-output behaviour of the process.

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Related Works

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Applications

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Main Results

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Quantum Comb

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=

Intermediate system

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Problem Formulation

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Quantum process

Interaction #1

Interaction #2

Intermediate system

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Efficient Causal Unravelling�Algorithm #1

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Criterion for Quantum Combs

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Independent

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Algorithm 1: A Recursive Algorithm

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Assumptions

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Accuracy and Complexity

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Algorithm 1: A Recursive Algorithm

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Independent

is a constant channel

Maximally entangled state

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Estimate each term with SWAP test (next slide)

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SWAP

Controlled-SWAP gate

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Summary of Algorithm 1

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Recursive causal unravelling algorithm

Criterion for last tooth

Independence test

Test of constant channel

Distance between states

SWAP test

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Efficient Causal Unravelling�Algorithm #2

WITH LOCAL STATE PREPARATION AND MEASUREMENTS

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Local State Preparation & Measurements

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Labels of chosen input states

Measurement outcomes

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Use Data for Testing Independence

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Case 2.1: Max # of Correlated Pairs

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=

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Algorithm 2.1

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Case 2.2: Independent Channels

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=

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Algorithm 2.2

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Summary

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Discussion

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Q & A

THANK YOU!

FULL PAPER - ARXIV: 2109.13166

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