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Heisenberg scaling with weak measurement: a quantum state discrimination point of view. (English) Zbl 1317.81013
Summary: We examine the results of the paper “Precision metrology using weak measurements” [L. Zhang et al., Phys. Rev. Lett. 114, 210801 (2015; doi:10.1103/PhysRevLett.114.210801)] from a quantum state discrimination point of view. The Heisenberg scaling of the photon number for the precision of the interaction parameter between coherent light and a spin one-half particle (or pseudo-spin) has a simple interpretation in terms of the interaction rotating the quantum state to an orthogonal one. To achieve this scaling, the information must be extracted from the spin rather than from the coherent state of light, limiting the applications of the method to phenomena such as cross-phase modulation. We next investigate the effect of dephasing noise and show a rapid degradation of precision, in agreement with general results in the literature concerning Heisenberg scaling metrology. We also demonstrate that a von Neumann-type measurement interaction can display a similar effect with no system/meter entanglement.

MSC:
81P15 Quantum measurement theory, state operations, state preparations
81P50 Quantum state estimation, approximate cloning
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[1] Aharonov, Y; Albert, DZ; Vaidman, L, How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, Phys. Rev. Lett., 60, 1351, (1988)
[2] Jordan, AN; Martínez-Rincón, J; Howell, JC, Technical advantages for weak-value amplification: when less is more., Phys. Rev. X, 4, 011031, (2014)
[3] Dressel, J; Malik, M; Miatto, FM; Jordan, AN; Boyd, RW, colloquium: understanding quantum weak values: basics and applications., Rev. Mod. Phys., 86, 307, (2014)
[4] Kofman, AG; Ashhab, S; Nori, F, Nonperturbative theory of weak pre- and post-selected measurements., Phys. Rep., 520, 43, (2012)
[5] Dressel, J; Lyons, K; Jordan, AN; Graham, TM; Kwiat, PG, Strengthening weak-value amplification with recycled photons., Phys. Rev. A, 88, 023821, (2013)
[6] Dowling, JP, Quantum optical metrology - the lowdown on high-N00N states., Contemp. Phys., 49, 125, (2008)
[7] Pang, S; Dressel, J; Brun, TA, Entanglement-assisted weak value amplification., Phys. Rev. Lett., 113, 030401, (2014)
[8] Wiseman, H.M., Milburn, G.J.: Quantum Measurement and Control. Cambridge University Press, Cambridge (2010) · Zbl 1350.81004
[9] Zilberberg, O; Romito, A; Starling, DJ; Howland, GA; Broadbent, CJ; Howell, JC; Gefen, Y, Null values and quantum state discrìmination., Phys. Rev. Lett., 110, 170405, (2013)
[10] Zhang, L., Datta, A., Walmsley, I.A.: Precision metrology using weak measurements. (2013). arXiv:1310.5302
[11] Murch, KW; Weber, SJ; Macklin, C; Siddiqi, I, Observing single quantum trajectories of a superconducting quantum bit., Nature, 502, 211, (2013)
[12] Weber, SJ; Chantasri, A; Dressel, J; Jordan, AN; Murch, KW; Siddiqi, I, Mapping the optimal route between two quantum states., Nature, 511, 570, (2014)
[13] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press Inc., New York (1976) · Zbl 1332.81011
[14] Braunstein, SL; Caves, CM; Milburn, GJ, Generalized uncertainty relations: theory, examples, and Lorentz invariance., Ann. Phys., 247, 135, (1996) · Zbl 0881.47046
[15] Ionicioiu, R; Terno, DR, Proposal for a quantum delayed-choice experiment., Phys. Rev. Lett., 107, 230406, (2011)
[16] Feizpour, A; Xing, X; Steinberg, AM, Amplifying single-photon nonlinearity using weak measurements., Phys. Rev. Lett., 107, 133603, (2011)
[17] Bardhan, BR; Jiang, K; Dowling, JP, Effects of phase fluctuations on phase sensitivity and visibility of path-entangled photon Fock states., Phys. Rev. A, 88, 023857, (2014)
[18] Hosten, O; Kwiat, P, Observation of the spin Hall effect of light via weak measurements., Science, 319, 787, (2008)
[19] Dixon, PB; Starling, DJ; Jordan, AN; Howell, JC, Ultrasensitive beam deflection measurement via interferometric weak value amplification., Phys. Rev. Lett., 102, 173601, (2009)
[20] Demkowicz-Dobrzański, R; Kolodyński, J; Guta, M, The elusive Heisenberg limit in quantum-enhanced metrology., Nat. Commun., 3, 1063, (2012)
[21] Escher, BM; Matos, RL, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. filho, and L. davidovich, Nat. Phys., 7, 406, (2011)
[22] Knysh, S; Smelyanskiy, VN; Durkin, GA, Scaling laws for precision in quantum interferometry and the bifurcation landscape of the optimal state., Phys. Rev. A, 83, 021804, (2011)
[23] Aspachs, M; Calsamiglia, J; Munoz-Tapia, R; Bagan, E, Phase estimation for thermal Gaussian states., Phys. Rev. A, 79, 033834, (2009)
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