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Title:           Quantum Theory in Finite Dimension Cannot Explain Every General Process with Finite Memory
Subject:         Communications in Mathematical Physics, https://doi.org/10.1007/s00220-023-04913-4
Author:          Marco Fanizza 
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      Title: Quantum Theory in Finite Dimension Cannot Explain Every General Process with Finite Memory
      Destination: Doc-Start
      Children: 
       Item: 
        Title: Abstract:
        Destination: neworcid.4
       Item: 
        Title: 1 Introduction
        Destination: section.1
       Item: 
        Title: 2 Results
        Destination: section.2
        Children: 
         Item: 
          Title: 2.1 Stationary stochastic processes and quasi-realizations
          Destination: subsection.2.1
         Item: 
          Title: 2.2 Classical and quantum processes
          Destination: subsection.2.2
         Item: 
          Title: 2.3 HMM vs HQMM
          Destination: subsection.2.3
         Item: 
          Title: 2.4 Processes without quantum realization
          Destination: subsection.2.4
       Item: 
        Title: 3 Discussion
        Destination: section.3
       Item: 
        Title: 4 Proofs
        Destination: section.4
        Children: 
         Item: 
          Title: 4.1 Quantum realizations of the FRDN processes: proof of Theorem 1
          Destination: subsection.4.1
          Children: 
           Item: 
            Title: 4.1.1 Quasi-realization
            Destination: subsubsection.4.1.1
           Item: 
            Title: 4.1.2 Quantum (completely positive) realization
            Destination: subsubsection.4.1.2
         Item: 
          Title: 4.2 Noise robustness of the size of classical memory: proof of Theorem 2
          Destination: subsection.4.2
         Item: 
          Title: 4.3 Processes without a quantum realization
          Destination: subsection.4.3
          Children: 
           Item: 
            Title: 4.3.1 Proof of Theorem 3: Exponential cone 
            Destination: subsubsection.4.3.1
           Item: 
            Title: 4.3.2 Proof of Theorem 4: Power cone
            Destination: subsubsection.4.3.2
       Item: 
        Title: Acknowledgements
        Destination: acksectcnt.1
       Item: 
        Title: References
        Destination: acksectcnt.1
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                           <pdfaProperty:description>ISSN for an electronic version of the issue in which the resource occurs. Permits publishers to include a second ISSN, identifying an electronic version of the issue in which the resource occurs (therefore e(lectronic)Issn. If used, prism:eIssn MUST contain the ISSN of the electronic version.</pdfaProperty:description>
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                           <pdfaProperty:description>The aggregation type specifies the unit of aggregation for a content collection. Comment PRISM recommends that the PRISM Aggregation Type Controlled Vocabulary be used to provide values for this element. Note: PRISM recommends against the use of the #other value currently allowed in this controlled vocabulary. In lieu of using #other please reach out to the PRISM group at info@prismstandard.org to request addition of your term to the Aggregation Type Controlled Vocabulary. </pdfaProperty:description>
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