Robert S Whitney 2008 J. Phys. A: Math. Theor. 41 175304 doi:10.1088/1751-8113/41/17/175304
Staying positive: going beyond Lindblad with perturbative master equations
Robert S Whitney
Show affiliationsThe perturbative master equation (Bloch–Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima–Zwanzig or Schoeller–Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch–Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.
- PACS
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03.67.Lx Quantum computation architectures and implementations
- MSC
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81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 17 (2 May 2008)
Received 1 November 2007, in final form 31 January 2008
Published 15 April 2008
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Staying positive: going beyond Lindblad with perturbative master equations
Robert S Whitney 2008 J. Phys. A: Math. Theor. 41 175304
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