Quantum-enhanced multiparameter estimation in multiarm interferometers

Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful particle (qudit) entanglement for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We theoretically discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.

[1]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[2]  A. Politi,et al.  Silica-on-Silicon Waveguide Quantum Circuits , 2008, Science.

[3]  Keiji Sasaki,et al.  Beating the Standard Quantum Limit with Four-Entangled Photons , 2007, Science.

[4]  John L. Hall,et al.  Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons , 1998 .

[5]  H. Yuen.  Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[6]  L. Pezzè,et al.  Entanglement, nonlinear dynamics, and the heisenberg limit. , 2007, Physical review letters.

[7]  S. Lloyd,et al.  Quantum metrology. , 2005, Physical review letters.

[8]  G Weihs,et al.  All-fiber three-path Mach-Zehnder interferometer. , 1996, Optics letters.

[9]  Z. Y. Ou,et al.  Engineering multiphoton entangled states by quantum interference , 2006 .

[10]  A. Politi,et al.  Manipulation of multiphoton entanglement in waveguide quantum circuits , 2009, 0911.1257.

[11]  Keiji matsumoto.  A new approach to the Cramér-Rao-type bound of the pure-state model , 2002 .

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

[13]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[14]  Nicolò Spagnolo,et al.  Three-photon bosonic coalescence in an integrated tritter , 2012, Nature Communications.

[15]  Augusto Smerzi,et al.  Ultrasensitive two-mode interferometry with single-mode number squeezing. , 2013, Physical review letters.

[16]  L. G. Helt,et al.  Tunable quantum interference in a 3D integrated circuit , 2014, Scientific Reports.

[17]  Roberta Ramponi,et al.  Three-dimensional Mach-Zehnder interferometer in a microfluidic chip for spatially-resolved label-free detection. , 2010, Lab on a chip.

[18]  Marco G. Genoni,et al.  Joint estimation of phase and phase diffusion for quantum metrology , 2014, Nature Communications.

[19]  Joachim Knittel,et al.  Biological measurement beyond the quantum limit , 2012, Nature Photonics.

[20]  S. Nolte,et al.  Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics , 2003 .

[21]  G. Aeppli,et al.  Proceedings of the International School of Physics Enrico Fermi , 1994 .

[22]  G. Marshall,et al.  Non-classical interference in integrated 3D multiports. , 2012, Optics express.

[23]  D L Snyder,et al.  Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy. , 1999, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  P. Humphreys,et al.  Quantum enhanced multiple phase estimation. , 2013, Physical review letters.

[25]  Augusto Smerzi,et al.  Useful multiparticle entanglement and sub-shot-noise sensitivity in experimental phase estimation. , 2011, Physical review letters.

[26]  A. Politi,et al.  Multimode quantum interference of photons in multiport integrated devices , 2010, Nature communications.

[27]  F. Illuminati,et al.  Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels , 2010, 1010.0442.

[28]  I. Walmsley,et al.  Experimental quantum-enhanced estimation of a lossy phase shift , 2009, 0906.3511.

[29]  J G Fujimoto,et al.  Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator. , 2005, Optics letters.

[30]  Nicolò Spagnolo,et al.  Quantum interferometry with three-dimensional geometry , 2012, Scientific Reports.

[31]  Holland,et al.  Interferometric detection of optical phase shifts at the Heisenberg limit. , 1993, Physical review letters.

[32]  Yusuke Nasu,et al.  Characterization of symmetric [3 x 3] directional couplers fabricated by direct writing with a femtosecond laser oscillator. , 2006, Optics express.

[33]  S. Lloyd,et al.  Advances in quantum metrology , 2011, 1102.2318.

[34]  Peter C Humphreys,et al.  Multiphoton quantum interference in a multiport integrated photonic device , 2012, Nature Communications.

[35]  Marco Barbieri,et al.  Multiparameter quantum metrology , 2012 .

[36]  Marco Barbieri,et al.  Tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry , 2012, 1206.0043.

[37]  Augusto Smerzi,et al.  Optimal measurements in phase estimation: simple examples , 2013, Quantum Inf. Process..

[38]  Hugo Cable,et al.  Quantum-enhanced tomography of unitary processes , 2014, 1402.2897.

[39]  G. Tóth,et al.  Multipartite entanglement and high precision metrology , 2010, 1006.4368.

[40]  Carl W. Helstrom,et al.  Noncommuting observables in quantum detection and estimation theory , 1974, IEEE Trans. Inf. Theory.

[41]  S. Braunstein,et al.  Statistical distance and the geometry of quantum states. , 1994, Physical review letters.

[42]  Animesh Datta,et al.  Quantum Enhanced Estimation of a Multidimensional Field. , 2015, Physical review letters.

[43]  Augusto Smerzi,et al.  Fisher information and multiparticle entanglement , 2010, 1006.4366.

[44]  Augusto Smerzi,et al.  Quantum theory of phase estimation , 2014, 1411.5164.

[45]  M. G. A. Paris,et al.  Optimal estimation of joint parameters in phase space , 2012, 1206.4867.

[46]  Horace P. Yuen,et al.  Multiple-parameter quantum estimation and measurement of nonselfadjoint observables , 1973, IEEE Trans. Inf. Theory.