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About this paper
Evan Borras
Deciding whether local Markovian quantum dynamics contains a decoherence-free state is shown to be computationally intractable in general. By connecting purity decay under a Lindbladian to a constrained separable Hamiltonian problem and constructing dissipative Feynman–Kitaev history states, the work proves QMA-completeness for constant-locality decay estimation and QMA^1-hardness for detecting pure steady states when the locality is at least five.
Key insights
- A pure steady state must satisfy stringent simultaneous eigenvector conditions for the jump operators; for Hermitian jumps, this reduces to being a common eigenstate of all of them.
- The decay rate of a pure state provides an energy-like quantity, while spectral-gap and projection arguments isolate the slowly decaying history-state sector from unwanted components.
- A one-dimensional decoherence-free subspace is already hard to detect, so the difficulty extends to the broader problem of finding arbitrary coherence-preserving subspaces.
Summary by alphaXiv.
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