Computing the Integrated Information of a Quantum Mechanism
Abstract
:1. Introduction
2. Theory
2.1. Classical Systems
2.1.1. Cause and Effect Repertoires
2.1.2. Intrinsic Difference (ID)
2.1.3. Identifying Intrinsic Causes and Effects
2.1.4. Disintegrating Partitions
2.1.5. Mechanism Integrated Information
2.2. Quantum Systems
2.2.1. Quantum Cause and Effect Repertoires
- If corresponds to a pure state, the purview qubits are fully determined by the mechanism qubits. Thus, is not influenced by qubits outside of m. It follows that if the latter is pure. This is analogous to the classical case, where if is deterministic.
- Conceptually, entangled subsets are treated as indivisible units in the effect repertoire. If a purview is fully entangled, then .
- Extraneous classical correlations are successfully discounted, which means they will not contribute to the integrated information of a mechanism (Figure 3).
2.2.2. Quantum Intrinsic Information (QID)
2.2.3. Identifying Intrinsic Causes and Effects
2.2.4. Disintegrating Partitions
2.2.5. Quantum Mechanism Integrated Information
2.2.6. The Intrinsic Structure of a Quantum System
3. Results
3.1. CNOT
3.1.1. Classical Case
3.1.2. Quantum Case
3.1.3. Mixed States and Extensions to Larger Systems
3.1.4. Intrinsic Structure Due to Entanglement
4. Discussion
4.1. Comparison with Previous Approaches
4.2. Measurement Dynamics
4.3. Formal Considerations and Limitations
4.4. From Micro to Macro?
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Albantakis, L.; Prentner, R.; Durham, I. Computing the Integrated Information of a Quantum Mechanism. Entropy 2023, 25, 449. https://doi.org/10.3390/e25030449
Albantakis L, Prentner R, Durham I. Computing the Integrated Information of a Quantum Mechanism. Entropy. 2023; 25(3):449. https://doi.org/10.3390/e25030449
Chicago/Turabian StyleAlbantakis, Larissa, Robert Prentner, and Ian Durham. 2023. "Computing the Integrated Information of a Quantum Mechanism" Entropy 25, no. 3: 449. https://doi.org/10.3390/e25030449