RT Journal Article T1 Intrinsic metrological resolution as a distance measure and nonclassical light A1 Rivas, Ángel A1 Luis Aina, Alfredo AB We elaborate on a Hilbert-Schmidt distance measure assessing the intrinsic metrological accuracy in the detection of signals imprinted on quantum probe states by signal-dependent transformations. For small signals this leads to a probe-transformation measure Lambda fully symmetric on the probe rho and the generator G of the transformation Λ(ρ,G)= Λ(G,ρ). Although Λ can be regarded as a generalization of variance, we show that no uncertainty relation holds for the product of measures corresponding to complementary generators. We show that all states with resolution larger than coherent states are nonclassical. We apply this formalism to feasible probes and transformations. PB American Physical Society SN 1050-2947 YR 2008 FD 2008-06-10 LK https://hdl.handle.net/20.500.14352/51486 UL https://hdl.handle.net/20.500.14352/51486 LA eng NO [1] W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, Phys. Rev. A 47, 3554 (1993); M. Hillery and L. Mlodinow, ibid. 48, 1548 (1993); D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, ibid. 50, 67 (1994); C. Brif and A. Mann, ibid. 54, 4505 (1996); Z. Y. Ou, ibid. 55, 2598 (1997); V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 96, 010401 (2006).[2] N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990); J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996); S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865 (1997); A. Luis, Phys. Rev. A 64, 054102) (2001); 65, 034102 (2002); Ph. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature (London) 429, 158 (2004); M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, ibid. 429, 161 (2004).[3] A. Luis, Phys. Rev. A 65, 025802 (2002); Phys. Lett. A 329, 8 (2004); Phys. Rev. A 69, 044101 (2004); 76, 035801 (2007); J. Opt. B: Quantum Semiclassical Opt. 6, 1 (2004); J. Beltrán and A. Luis, Phys. Rev. A 72, 045801 (2005); S. M. Roy and S. L. Braunstein, e-print arXiv:quant-ph/0607152, Phys. Rev. Lett. (to be published); S. Boixo, S. T. Flammia, C. M. Caves, and J. M. Geremia, Phys. Rev. Lett. 98, 090401 (2007); S. Boixo, A. Datta, S. T. Flammia, A. Shaji, E. Bagan, and C. M. Caves, Phys. Rev. A 77, 012317 (2008).[4] S. Luo and Q. Zhang, Phys. Rev. A 69, 032106 (2004).[5] S. Luo, Phys. Rev. Lett. 91, 180403 (2003).[6] V. V. Dodonov, O. V. Man’ko, V. I. Man’ko, and A. Wünsche, J. Mod. Opt. 47, 633 (2000); V. V. Dodonov and M. B. Renó, Phys. Lett. A 308, 249 (2003).[7] J. Lee, M. S. Kim, and Č. Brukner, Phys. Rev. Lett. 91, 087902 (2003); R. Filip, Phys. Rev. A 65, 062320 (2002); M. Hendrych, M. Dušek, R. Filip, and J. Fiurášek, Phys. Lett. A 310, 95 (2003).[8] V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. 78, 2275 (1997); V. Vedral and M. B. Plenio, Phys. Rev. A 57, 1619 (1998); C. Witte and M. Trucks, Phys. Lett. A 257, 10 (1998); M. Ozawa, ibid. 268, 158 (2000).[9] S. A. Ponomarenko and E. Wolf, Opt. Lett. 26, 122 (2001).[10] S. Chountasis and A. Vourdas, Phys. Rev. A 58, 1794 (1998); S. A. Ponomarenko and E. Wolf, ibid. 63, 062106 (2001); A. Vourdas, ibid. 69, 022108 (2004).[11] M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984); M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997); L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, England, 1995).[12] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000); M. Hayashi, Quantum Information: An Introduction (Springer-Verlag, Berlin, 2006).[13] Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988); L. M. Johansen and A. Luis, Phys. Rev. A 70, 052115 (2004).[14] S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 72, 3439 (1994).[15] S. Luo, Proc. Am. Math. Soc. 132, 885 (2004).[16] S. Luo, Phys. Rev. A 72, 042110 (2005).[17] This is essentially because Eq. (2.28) is derived in Ref. (5) from a nonpositive definite inner product.[18] S. Zozor, M. Portesi, and Ch. Vignat, e-print arXiv:math.PR/0709.3011. NO ©2008 The American Physical Society. A.R. acknowledges financial support from the University of Hertfordshire and the EU Integrated Project QAP. A.L. acknowledges support from the Universidad Complutense Project No. PR1-A/07-15378. NO University of Hertfordshire NO Unión Europea (UE) NO Universidad Complutense de Madrid (UCM) DS Docta Complutense RD 27 abr 2024