Quantum metrology with open dynamical systems

This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical force sensing. When optical loss is present, these bounds are found to obey shot-noise scalings for arbitrary quantum states of light under certain realistic conditions, thus ruling out the possibility of asymptotic Heisenberg error scalings with respect to the average photon flux under those conditions. The proposed bounds are expected to be approachable using current quantum optics technology.

[1]  C. Caves,et al.  Coherent quantum-noise cancellation for optomechanical sensors. , 2010, Physical review letters.

[2]  Mankei Tsang,et al.  Time-symmetric quantum theory of smoothing. , 2009, Physical review letters.

[3]  Hidehiro Yonezawa,et al.  Quantum-limited mirror-motion estimation. , 2013, Physical review letters.

[4]  L. Davidovich,et al.  Quantum Metrology for Noisy Systems , 2011 .

[5]  Carlton M. Caves,et al.  Evading quantum mechanics , 2012, 1203.2317.

[6]  Mankei Tsang,et al.  Ziv-Zakai error bounds for quantum parameter estimation. , 2011, Physical review letters.

[7]  Saikat Guha,et al.  Realizable receivers for discriminating coherent and multicopy quantum states near the quantum limit , 2012, 1212.2048.

[8]  Robert L. Cook,et al.  Optical coherent state discrimination using a closed-loop quantum measurement , 2007, Nature.

[9]  T. Kippenberg,et al.  Cavity Optomechanics: Back-Action at the Mesoscale , 2008, Science.

[10]  N. Mavalvala,et al.  Quantum metrology for gravitational wave astronomy. , 2010, Nature communications.

[11]  Steven Chu.  Cold Atoms and Quantum Control , 2002 .

[12]  Ranjith Nair,et al.  Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection , 2011, 1105.4063.

[13]  Vladimir B. Braginsky,et al.  Quantum Measurement , 1992 .

[14]  C. Gardiner.  Stochastic Methods: A Handbook for the Natural and Social Sciences , 2009 .

[15]  S. Lloyd,et al.  Minimum output entropy of bosonic channels: A conjecture , 2004, quant-ph/0404005.

[16]  R. Gilmore.  Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists , 2008 .

[17]  E H Huntington,et al.  Adaptive optical phase estimation using time-symmetric quantum smoothing. , 2009, Physical review letters.

[18]  Vadim N. Smelyanskiy,et al.  Scaling laws for precision in quantum interferometry and the bifurcation landscape of the optimal state , 2010, 1006.1645.

[19]  C. Helstrom.  Quantum detection and estimation theory , 1969 .

[20]  K. Kraus,et al.  States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin , 1983 .

[21]  Klaus Molmer,et al.  Estimation of fluctuating magnetic fields by an atomic magnetometer (8 pages) , 2006, quant-ph/0605237.

[22]  Harry L. Van Trees,et al.  Detection, Estimation, and Modulation Theory, Part I , 1968 .

[23]  Markus Aspelmeyer,et al.  Quantum optomechanics—throwing a glance [Invited] , 2010, 1005.5518.

[24]  Adam Paszkiewicz,et al.  On quantum information , 2012, ArXiv.

[25]  H. M. Wiseman,et al.  Adaptive quantum measurements of a continuously varying phase , 2002 .

[26]  M. Paris.  Quantum estimation for quantum technology , 2008, 0804.2981.

[27]  M. Tsang.  Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing , 2009, 0906.4133.

[28]  Carlton M. Caves,et al.  Fundamental quantum limit to waveform estimation , 2010, CLEO: 2011 - Laser Science to Photonic Applications.

[29]  Seth Lloyd,et al.  Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time , 2008, 0902.3034.

[30]  Jan Kolodynski,et al.  Phase estimation without a priori phase knowledge in the presence of loss , 2010, 1006.0734.

[31]  S. Lloyd,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004, Science.

[32]  G M D'Ariano,et al.  Using entanglement improves the precision of quantum measurements. , 2001, Physical review letters.

[33]  Shuntaro Takeda,et al.  Quantum-Enhanced Optical-Phase Tracking , 2012, Science.

[34]  David Blair,et al.  A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application , 2011, 1109.2295.

[35]  D. Budker,et al.  Optical magnetometry - eScholarship , 2006, physics/0611246.

[36]  Saikat Guha,et al.  SymmetricM-ary phase discrimination using quantum-optical probe states , 2012, 1206.0673.

[37]  M B Plenio,et al.  Quantum speed limits in open system dynamics. , 2012, Physical review letters.

[38]  Yanbei Chen,et al.  Macroscopic quantum mechanics: theory and experimental concepts of optomechanics , 2013, 1302.1924.

[39]  Mark M. Wilde,et al.  From Classical to Quantum Shannon Theory , 2011, ArXiv.

[40]  Andrey B. Matsko,et al.  Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics , 2001 .

[41]  Thomas H. Seligman,et al.  Dynamics of Loschmidt echoes and fidelity decay , 2006, quant-ph/0607050.

[42]  S. Lloyd.  Enhanced Sensitivity of Photodetection via Quantum Illumination , 2008, Science.

[43]  Jan Kolodynski,et al.  Efficient tools for quantum metrology with uncorrelated noise , 2013, 1303.7271.

[44]  L. Davidovich,et al.  General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology , 2011, 1201.1693.

[45]  Hiroshi Imai,et al.  A fibre bundle over manifolds of quantum channels and its application to quantum statistics , 2008 .

[46]  S. Lloyd,et al.  Quantum illumination with Gaussian states. , 2008, Physical review letters.

[47]  H.M. Wiseman,et al.  Adaptive phase measurements for narrowband squeezed beams , 2006, 2006 Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference.

[48]  Kristine L. Bell,et al.  Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking , 2007 .

[49]  M. M. Taddei,et al.  Quantum Speed Limit for Physical Processes , 2013 .

[50]  Interferometry as a binary decision problem , 1996, quant-ph/9611035.

[51]  Helmut Ritsch,et al.  Quantum optics with ultracold quantum gases: towards the full quantum regime of the light–matter interaction , 2012, 1203.0552.

[52]  L. Davidovich,et al.  Quantum metrological limits via a variational approach. , 2012, Physical review letters.

[53]  Stefano Pirandola,et al.  Quantum Reading of a Classical Digital Memory , 2011, Physical review letters.

[54]  Robert Gilmore,et al.  Lie Groups, Physics, and Geometry: Frontmatter , 2008 .

[55]  Seth Lloyd,et al.  Quantum theory of optical temporal phase and instantaneous frequency , 2008 .

[56]  Masahide Sasaki,et al.  Quantum receiver beyond the standard quantum limit of coherent optical communication. , 2011, Physical review letters.

[57]  R. Nair,et al.  Fundamental Quantum Limits to Waveform Detection , 2012, 1204.3697.

[58]  Ou.  Complementarity and Fundamental Limit in Precision Phase Measurement. , 1996, Physical review letters.

[59]  Rafał Demkowicz-Dobrzański,et al.  The elusive Heisenberg limit in quantum-enhanced metrology , 2012, Nature Communications.

[60]  M. Nussbaum,et al.  Asymptotic Error Rates in Quantum Hypothesis Testing , 2007, Communications in Mathematical Physics.

[61]  Mankei Tsang.  Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing , 2009 .

[62]  Masahide Sasaki,et al.  Demonstration of near-optimal discrimination of optical coherent states. , 2008, Physical review letters.

[63]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.