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Purification Complexity without Purifications

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arxiv 2006.01088 v1 pith:OYTZUNBA submitted 2020-06-01 hep-th quant-ph

Purification Complexity without Purifications

classification hep-th quant-ph
keywords complexitypurificationmetricquantumstatesexplicitlyfubini-studywithout
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric on the space of density matrices as the complexity measure. Due to Uhlmann's theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly illustrate our conclusions for purification complexity.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Geometry of Quantum Complexity in Open Systems

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    Introduces tripartite complexity and complexity gap for three-region subsystems and reports that the gap has a definite sign in holographic volume complexity, Fisher-Rao Gaussian complexity, and Krylov-space approaches.

  3. Complexity Inequalities for Quantum Subsystems

    hep-th 2026-06 unverdicted novelty 7.0

    Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for comp...