Geometric Decoherence Time in Lindbladian Dynamics

• URL: http://arxiv.org/abs/2606.02743v1
• Date: Mon, 01 Jun 2026 18:06:40 GMT
• Title: Geometric Decoherence Time in Lindbladian Dynamics
• Abstract summary: We introduce the $geometric$ $decoherence$ $time$, defined as the earliest moment the monotone relation between logarithmic negativity and Rényi-$tfrac1212 entropy.<n>We show that quantum mutual information provides a complementary long-time diagnostic.<n>Our results establish a dynamical scale tracking the onset of decoherence.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The onset of decoherence in open many-body systems lacks a dynamical timescale grounded in the loss of bipartite entanglement. Here, we introduce the $geometric$ $decoherence$ $time$, defined as the earliest moment the monotone relation between logarithmic negativity and Rényi-$\tfrac{1}{2}$ entropy -- exactly equal across any bipartition for pure states -- breaks down under open-system evolution, signaling entropy growth without accompanying entanglement growth. We establish this criterion in both single-particle Gaussian dynamics and many-body Lindbladian evolution. We show that quantum mutual information provides a complementary long-time diagnostic: its asymptotic vanishing is equivalent to factorization of the steady state across the bipartition, a condition strictly stronger than separability, and whenever a product steady state is approached exponentially in trace norm, negativity and mutual information share the same decay rate. In the presence of a strong symmetry, this tracking can fail -- residual classical correlations can survive after entanglement has vanished. In the Kitaev chain with balanced gain and loss, we derive a closed-form solution and show that the topological phase sustains longer coherence times than the trivial phase at identical dissipation, with a local minimum at the chiral-symmetric point. In the interacting XXZ chain, exact many-body evolution shows that local $Z$-dephasing preserves residual classical correlations, whereas gain and loss restore the mutual-information tracking of negativity. Our results establish the geometric decoherence time as a dynamical scale tracking the onset of decoherence.

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