Inequalities of operator valued quantum skew information
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we study two operator-valued inequalities for quantum Wigner-Yanase-Dyson skew information related to module operators. These are extended results of the trace inequalities for Wigner-Yanase-Dyson skew information. Moreover, we study a sufficient condition to prove an uncertainty relation for operator-valued generalized quantum Wigner-Yanase-Dyson skew information related to module operators and a pair of functions $(f, g)$. Also, we obtain several previous results of scalar-valued cases as a consequence of our main result.
Abstract
In this paper, we study two operator-valued inequalities for quantum Wigner-Yanase-Dyson skew information related to module operators. These are extended results of the trace inequalities for Wigner-Yanase-Dyson skew information. Moreover, we study a sufficient condition to prove an uncertainty relation for operator-valued generalized quantum Wigner-Yanase-Dyson skew information related to module operators and a pair of functions $(f, g)$. Also, we obtain several previous results of scalar-valued cases as a consequence of our main result.
참고문헌 (15)
- Byoung Jin Choi, "Inequalities for positive module operators on von Neumann algebras", Journal of Mathematical Physics, 59(6), pp.063513~ (2018), AIP Publishing[DOI]
- Ali Dadkhah, "Quantum information inequalities via tracial positive linear maps", Journal of Mathematical Analysis and Applications, 447(1), pp.666~680 (2017), Elsevier BV[DOI]
- Ali Dadkhah, "Noncommutative versions of inequalities in quantum information theory", Analysis and Mathematical Physics, 9(4), pp.2151~2169 (2019), Springer Science and Business Media LLC[DOI]
- Jun Ichi Fujii, "A trace inequality arising from quantum information theory", Linear Algebra and its Applications, 400, pp.141~146 (2005), Elsevier BV[DOI]
- Shigeru Furuichi, "Inequalities for Tsallis relative entropy and generalized skew information", Linear and Multilinear Algebra, 59(10), pp.1143~1158 (2011), Informa UK Limited[DOI]
- Shigeru Furuichi, "Schrödinger uncertainty relation, Wigner–Yanase–Dyson skew information and metric adjusted correlation measure", Journal of Mathematical Analysis and Applications, 388(2), pp.1147~1156 (2012), Elsevier BV[DOI]
- S. Furuichi, "Trace inequalities on a generalized Wigner–Yanase skew information", Journal of Mathematical Analysis and Applications, 356(1), pp.179~185 (2009), Elsevier BV[DOI]
- Paolo Gibilisco, "Uncertainty principle and quantum Fisher information", Annals of the Institute of Statistical Mathematics, 59(1), pp.147~159 (2007), Springer Science and Business Media LLC[DOI]
- W. Heisenberg, "Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und ¨Mechanik", Z. Phys, 43, pp.172~198 (1927)
- Chul Ki Ko, "Uncertainty relation associated with a monotone pair skew information", Journal of Mathematical Analysis and Applications, 383(1), pp.208~214 (2011), Elsevier BV[DOI]
- Chul Ki Ko, "Schrödinger uncertainty relation and convexity for the monotone pair skew information", Tohoku Mathematical Journal, 66(1), pp.107~117 (2014), Mathematical Institute, Tohoku University[DOI]
- S. Luo, "Heisenberg uncertainty relation for mixed states", Phys. Rev. A, 72, pp.04~ (2005)
- Yong Moon Park, "Improvement of uncertainty relations for mixed states", Journal of Mathematical Physics, 46(4), pp.042109~ (2005), AIP Publishing[DOI]
- E. Schr¨odinger, "About Heisenberg uncertainty relation", Bulgar. J. Phys, 26, pp.193~203 (1999)
- K. Yanagi, "A Generalized Skew Information and Uncertainty Relation", IEEE Transactions on Information Theory, 51(12), pp.4401~4404 (2005), Institute of Electrical and Electronics Engineers (IEEE)[DOI]