Quantum Information Processing

, Volume 15, Issue 3, pp 1025–1042 | Cite as

On the connection between quantum nonlocality and phase sensitivity of two-mode entangled Fock state superpositions

  • Kaushik P. Seshadreesan
  • Christoph F. Wildfeuer
  • Moochan B. Kim
  • Hwang Lee
  • Jonathan P. Dowling


In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form \((|N-m\rangle _a|m\rangle _b+\mathrm{e}^{i (N-2m)\phi }|m\rangle _a|N-m\rangle _b)/\sqrt{2}\) have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state \((|N\rangle _a|0\rangle _b+\mathrm{e}^{i N\phi }|0\rangle _a|N\rangle _b)/\sqrt{2}\) and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.


Quantum information Quantum entanglement Bell tests 



J. P. D. and K. P. S. would like to acknowledge support from the Air Force Office of Scientific Research, the Army Research Office, the Defense Advanced Research Projects Agency, and the National Science Foundation. C. F. W. would like to add the following acknowledgment: I first met Howard at QCMC 2002 in Boston. He told me that as part of his formal education he went to the south of Germany and attended High School for a couple of years. He enjoyed chatting in German with me. Howard also introduced me to Jonathan P. Dowling at this conference who later hired me as a post doc. I met Howard several times at various international conferences over the past years. He always gave me advice on career moves and research topics, even in the weeks before his surgery. His encouragement and generosity made a deep impression on me, and I will never forget this extraordinary researcher and warm welcoming personality.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Kaushik P. Seshadreesan
    • 1
  • Christoph F. Wildfeuer
    • 2
  • Moochan B. Kim
    • 3
  • Hwang Lee
    • 1
  • Jonathan P. Dowling
    • 1
  1. 1.Department of Physics and Astronomy, Hearne Institute for Theoretical PhysicsLouisiana State UniversityBaton RougeUSA
  2. 2.Institute of Mathematics and Natural SciencesUniversity of Applied Sciences and Arts Northwestern SwitzerlandWindischSwitzerland
  3. 3.Institute for Quantum Science and Engineering and Department of Physics and AstronomyTexas A&M UniversityCollege StationUSA

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