Beyond complete positivity

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• 作者：Jason M. Dominy ; Daniel A. Lidar
• 关键词：Complete positivity ; Quantum maps ; Non ; completely positive dynamics ; Quantum subsystem dynamics
• 刊名：Quantum Information Processing
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：15
• 期：4
• 页码：1349-1360
• 全文大小：469 KB
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  45.Note that this formulation includes no consideration as to how or why the initial state came to be in \({\cal D}_{\text{ SB }}\cap {\cal V}\) ; it only models how the subsystem state changes from this point forward. If one wishes to also model state preparation or other prior evolution, the map(s) representing those prior steps should be precomposed with \(\Psi _{U}^{{\cal V}}\) (and will also strongly influence the choice of \({\cal V}\) ) [42]
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• 作者单位：Jason M. Dominy (1) (4)
  Daniel A. Lidar (1) (2) (3) (4)
  
  1. Department of Chemistry, University of Southern California, Los Angeles, CA, 90089, USA
  4. Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, CA, 90089, USA
  2. Department of Physics, University of Southern California, Los Angeles, CA, 90089, USA
  3. Department of Electrical Engineering, University of Southern California, Los Angeles, CA, 90089, USA
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

文摘

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any \({\mathbb {C}}\)-linear, Hermiticity-preserving, trace-preserving map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application, we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality.