Surprising Spectral Gap and Entropy Decay Estimates in Open Quantum Systems with a Large Number of Qubits

• URL: http://arxiv.org/abs/2209.11099v1
• Date: Thu, 22 Sep 2022 15:36:47 GMT
• Title: Surprising Spectral Gap and Entropy Decay Estimates in Open Quantum Systems with a Large Number of Qubits
• Authors: Yidong Chen and Marius Junge
• Abstract summary: We study the spectral gap and modified logarithmic Sobolev constant of some very simple open systems given by a representation of $mathfraksu(2)$ on N-qubits. Our examples fall into the class of Lindbladians admissible to the dissipative quantum Church-Turing thesis arXiv:1105.3986.
• Score: 6.680567488352617
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the major challenges in quantum information science is to control systems with a large number of qubits. Since any realistic quantum system interacts with the environment, it is important to have quantitative estimates on decoherence. The time evolution of an open quantum system can be modeled by a Lindbladian obtained by tracing out the environment degrees of freedom and performing a Born-Markov approximation. In this paper we study the spectral gap and modified logarithmic Sobolev constant of some very simple open systems given by a representation of $\mathfrak{su}(2)$ on N-qubits. Our examples fall into the class of Lindbladians admissible to the dissipative quantum Church-Turing thesis arXiv:1105.3986. In addition, our examples can also be written as Davies generators. Moreover, the main example has a dimension-dependent spectral gap at finite temperature. This is complementary to the class of Davies generators in arXiv:1409.3435, where local spectral estimates automatically imply global ones.

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