Quantum state transformation by optimal projective measurements

Yaoxiong Wang, Rebing Wu, Xin Chen, Yunjian Ge, Junhui Shi, Herschel Albert Rabitz, Feng Shuang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

This paper explores the optimal control of quantum state transformations in finite-dimensional quantum systems by a sequence of non-selective projective measurements. In our schemes, the projectors of each measurement are represented by a unitary matrix. Through variational analysis of the objective function over the unitary group, the necessary condition for a measurement sequence to be a critical point of the underlying state transformation objective is found to be a highly symmetric form as a chain of equalities. Since these equality relations are generally difficult to solve analytically, we focus on the fundamental case employing a single measurement, in which analytical solutions for maximizing the state transformation probability are found between pure states, or between mixed and pure states, or between orthogonal mixed states under two typical type of measurements. These results suggest a new way of designing optimal quantum dynamics control strategies by quantum measurements.

Original languageEnglish (US)
Pages (from-to)507-519
Number of pages13
JournalJournal of Mathematical Chemistry
Volume49
Issue number2
DOIs
StatePublished - Jan 1 2011

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Applied Mathematics

Keywords

  • Optimal control
  • Projective measurement
  • Quantum control
  • Quantum measurement

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