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<p>We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-tensor category of the final state is a braided <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-tensor subcategory of the initial state.</p>

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Mixed State Topological Order: Operator Algebraic Approach

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Yoshiko Ogata

摘要

We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided \(C^*\) C ∗ -tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided \(C^*\) C ∗ -tensor category of the final state is a braided \(C^*\) C ∗ -tensor subcategory of the initial state.