Study of Conditional SIC-POVM

• Project/Area Number: 25800061
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Shinshu University
• Principal Investigator: OHNO Hiromichi 信州大学, 学術研究院工学系, 准教授 (90554585)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 量子情報理論 / 量子トモグラフィー / 正作用素値測度

Outline of Final Research Achievements

The state of a quantum system is a density matrix with several parameters. The concern is how to recover the parameters. Several possibilities exist for the optimal recovery method, and we consider some special cases. We assume that a few parameters are known and that the others are to be recovered. The optimal positive operator valued measure (POVM) for recovering unknown parameters with an additional condition is called a conditional symmetric informationally complete POVM (SIC-POVM). We study the existence or nonexistence of conditional SIC-POVMs. We provide a necessary condition for existence and some examples.

Research Products

• [Int'l Joint Research] Alfred Renyi Institute of Mathematics(ハンガリー)
• [Journal Article] Non-commutative hypergroup of order five (2017)
  • Author(s): Yasumichi Matsuzawa, Hiromichi Ohno, Akito Suzuki, Tatsuya Tsurii, Satoe Yamanaka
  • Journal Title: Journal of Algebra and Applications Volume: 印刷中 Issue: 07 Pages: 1750127-1750127
  • DOI: 10.1142/s0219498817501274
  • NAID: 120007100052
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Unitary equivalent classes of one-dimensional quantum walks (2016)
  • Author(s): Hiromichi Ohno
  • Journal Title: Quantum Information Processing Volume: 15 Issue: 9 Pages: 3599-3617
  • DOI: 10.1007/s11128-016-1361-5
  • NAID: 120007100053
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Examples of conditional SIC-POVMs (2015)
  • Author(s): Hiromichi Ohno, Denes Petz
  • Journal Title: Quantum Information Processing Volume: 14 Issue: 10 Pages: 3983-3999
  • DOI: 10.1007/s11128-015-1085-y
  • NAID: 120007101502
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] 1次元量子ウォークのユニタリ同値性について (2016)
  • Author(s): 大野 博道
  • Organizer: 日本数学会2016年度秋季総合分科会
  • Place of Presentation: 関西大学
  • Year and Date: 2016-09-15
• [Presentation] Unitary equivalent classes of one-dimensional quantum walks (2016)
  • Author(s): Hiromichi Ohno
  • Organizer: RIMS研究集会「作用素環論の最近の進展」
  • Place of Presentation: 京都大学
  • Year and Date: 2016-09-12
  • Int'l Joint Research
• [Presentation] 条件付きSIC－POVMとその例 (2015)
  • Author(s): 大野 博道
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: KKR妙高高原 白樺荘（新潟県）
  • Year and Date: 2015-10-24
• [Presentation] Existence of conditional SIC-POVM (2015)
  • Author(s): Hiromichi Ohno
  • Organizer: Workshop on Quantum Information Theory and Related Topics
  • Place of Presentation: Hanoi, Vietnam
  • Year and Date: 2015-09-01
  • Int'l Joint Research
• [Presentation] A new approach to quantum state tomography (2014)
  • Author(s): Hiromichi Ohno
  • Organizer: Workshop on quantum information theory and related topics
  • Place of Presentation: 立命館大学
  • Year and Date: 2014-09-04 – 2014-09-06
• [Presentation] Necessary condition for existence of conditional SIC-POVM (2014)
  • Author(s): Hiromichi Ohno
  • Organizer: RIMS研究集会 不確実さと曖昧さの数理
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Examples of conditional SIC-POVM (2013)
  • Author(s): Hiromichi Ohno
  • Organizer: The first international workshop on quantum information theory and related topics
  • Place of Presentation: Duy Tan University, Da Nang, Viet Nam
• [Remarks] SOAR 研究者総覧｜信州大学学術情報オンラインシステムSOAR
  • URL: http://soar-rd.shinshu-u.ac.jp/profile/ja.yFTmbpkh.html