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Complexity for Open Quantum System
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Complexity for Open Quantum System
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We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix by tracing out the bath degrees of freedom for both regular and inverted oscillator and computed the complexity of purification (COP) and complexity by using the operator-state mapping. We found that when the oscillator is regular the COP saturates quickly for both underdamped and overdamped oscillators. Interestingly, when the oscillator is underdamped, we discover a kink like behaviour for the saturation value of COP with varying damping coefficient. For the inverted oscillator, we found a linear growth of COP with time for all values of bath-system interaction. However, when the interaction is increased the slope of the linear growth decreases, implying that the unstable nature of the system can be regulated by the bath.
Forward citations
Cited by 3 Pith papers
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The Geometry of Quantum Complexity in Open Systems
Nielsen complexity for Lindbladian open systems induces a sub-Finslerian geometry on mixed states whose flag curvature depends on control penalty factors.
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A Landscape of Cosmological Decoherence
A geometric landscape of mixed states for cosmological perturbations unifies decoherence models and derives non-linearity bounds that rule out decohered thermal states and limit amplitude-diagonal models to under 70 e...
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Krylov Complexity for Open Quantum System: Dissipation and Decoherence
Krylov complexity saturates in the full high-temperature Caldeira-Leggett system, reproduces dissipative features when decoherence is suppressed, shows oscillations when dissipation is suppressed, and remains insensit...
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