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“Quantum Liang Information Flow as Causation Quantifier”

The past decade has seen a series of studies by Prof. X.S. Liang on the theory of information flow and the information flow-based causality analysis. Rigorously established from first principles, the formalism is built on a solid foundation of mathematics and physics. It has since been applied to different disciplines including but not limited to climate prediction, neuroscience and artificial intelligence. Recently, this formalism has been further extended to the quantum domain by scientists from University College--London.

At the quantum level, the violation of Bell’s inequality is well known to have broken down the classical notion of cause and effect. Consequently, quantum causality quantification reemerged as a fundamental issue. To this end, correlation functions of a Heisenberg picture in evolving operators are usually used to ascertain casual influences in quantum environments. However, as stated in a mathematical formula by Liang, correlation does not imply causation. Caution must be exercised to interpret the correlation-based results of causation.

To ascertain accurate quantum causality, Bin Yi and Sougato Bose generalized the above information flow to the quantum domain with respect to von Neumann entropy. They referred to the thus-obtained information flow as the quantum Liang information flow. Moreover, the approach to freeze a node to obtain its causal influence on other nodes in a network, as invented in Liang’s formalism, is also exploited in this work to construct causal networks within quantum systems, especially those with entanglement.

Several interesting conclusions were drawn in their paper. For example, for a two-qubit system in bosonic bath where the noninteracting qubits coupled with the reservoir with different strengths, the information flow between the two qubits were found to be nontrivial. While the information flow from the weakly coupled one had a higher rate, that from the strongly coupled one was greater in cumulative form in the long run (cf., Fig. 1). For multi-qubit system, they found that the addition of a strong coupling between qubits into a five-qubit network diverted the directions of uncertainty propagation, as shown in Fig. 2.

Figure 1 (Fig. 4 in the article). (a) Rate of
information flow (in bits per unit time) and (b) cumulative information flow (in
bits) within the two-qubit system in a lossy cavity. Blue curves: from B to A.
Orange curves: from A to B. Coupling strength ratio *α _{A}/α_{B}*=10/1.

Figure 2 (Fig. 3 in the article). Cumulative
information flow (in bits) toward the center *E* in the five-qubit network
(a) from any sending qubit with identical coupling strength: *η _{DE}=η_{CE}=η_{BE}=η_{AE}*=1
and (b) from A or B (orange curve) and C or D (blue curve) with additional
coupling

*η*=5.

_{CD}

The paper has been published In the top-notch
journal in physics, *Physical Review Letters*. The following is
the citation:

Yi, B., & Bose, S. (2022). Quantum Liang Information Flow as Causation Quantifier. *Phys.
Rev. Lett.*, 129(2), 020501. https://link.aps.org/doi/10.1103/PhysRevLett.129.020501.