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Quantum information in the Posner model of quantum cognition

Yunger Halpern, Nicole and Crosson, Elizabeth (2019) Quantum information in the Posner model of quantum cognition. Annals of Physics, 407 . pp. 92-147. ISSN 0003-4916. http://resolver.caltech.edu/CaltechAUTHORS:20171122-084552130

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Abstract

Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times. The spins would serve as biological qubits. The qubits may resist decoherence longer when in Posner molecules. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we construct applications of biological qubits to quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model’s quantum-communication ability, we show how it can teleport information incoherently: A state’s weights are teleported. Dephasing results from the entangling operation’s simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model’s operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck–Kennedy–Lieb–Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). Finally, we show that entanglement can affect molecular-binding rates, boosting a binding probability from 33.6% to 100% in an example. This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.aop.2018.11.016DOIArticle
https://arxiv.org/abs/1711.04801arXivDiscussion Paper
ORCID:
AuthorORCID
Yunger Halpern, Nicole0000-0001-8670-6212
Alternate Title:Quantum information in quantum cognition
Additional Information:© 2018 Published by Elsevier Inc. Received 29 June 2018, Accepted 16 November 2018, Available online 26 November 2018. We thank Ning Bao, Philippe Faist, Matthew Fisher, Steve Flammia, Yaodong Li, Leo Radzihovsky, and Tzu-Chieh Wei for discussions. We thank Fernando Pastawski for help with constructing the quantum error-detecting code. NYH thanks John Preskill for nudges toward this paper’s topic and for feedback about drafts. We are grateful for funding from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support from the Gordon and Betty Moore Foundation (GBMF-2644). This research was partially supported by the NSF also under Grant No. NSF PHY-1125915. NYH is grateful for partial support from the Walter Burke Institute for Theoretical Physics at Caltech, for a Graduate Fellowship from the Kavli Institute for Theoretical Physics, for a Barbara Groce Graduate Fellowship, and for an NSF grant for the Institute for Theoretical Atomic, Molecular, and Optical Physics at Harvard University and the Smithsonian Astrophysical Observatory.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
NSFPHY-1125915
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Kavli Institute for Theoretical PhysicsUNSPECIFIED
Barbara Groce Graduate Fellowship, CaltechUNSPECIFIED
Subject Keywords:Quantum information processing; Quantum computation; Quantum entanglement; Measurement-based quantum computation; Quantum teleportation; Posner molecule; Quantum error correction
Record Number:CaltechAUTHORS:20171122-084552130
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171122-084552130
Official Citation:Nicole Yunger Halpern, Elizabeth Crosson, Quantum information in the Posner model of quantum cognition, Annals of Physics, Volume 407, 2019, Pages 92-147, ISSN 0003-4916, https://doi.org/10.1016/j.aop.2018.11.016. (http://www.sciencedirect.com/science/article/pii/S0003491618303014)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83426
Collection:CaltechAUTHORS
Deposited By: Bonnie Leung
Deposited On:27 Nov 2017 17:54
Last Modified:17 May 2019 03:56

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