[Qirg] applications: reference frames

[Rodney Van Meter <[e-mail]>]

Chonggang,

A few references you might want to be familiar with for your applications draft.  I’m not saying “please cite all of these”, but you should probably familiarize yourself with them.  Note that the interface between the Bell pairs (or other distributed states) and the cybernetic system that maintains the relationship to the real world (e.g., up v. down, east v. west, time) is not clear.  Bell pairs are essentially digital, so a lot of work needs to be put in to figure out how to map those states to an outside frame of reference.  But if it can be done, then distributed states will serve as exquisitely sensitive reference frames, improving distributed sensing, including hopefully topics such as long-baseline interferometry (n.b.: there is some controversy over whether the interferometry use works with ordinary, thermal light like that coming from stars, or whether it only works with coherent light, like that coming from lasers).


@article{RevModPhys.79.555,
  title = {Reference frames, superselection rules, and quantum information},
  author = {Bartlett, Stephen D. and Rudolph, Terry and Spekkens, Robert W.},
  journal = {Rev. Mod. Phys.},
  volume = {79},
  issue = {2},
  pages = {555--609},
  numpages = {0},
  year = {2007},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/RevModPhys.79.555},
  url = {http://link.aps.org/doi/10.1103/RevModPhys.79.555},
  comment = {Cited by Islam for being important in two-party reference frames.}
}

@article{PhysRevLett.87.167901,
  title = {Transmission of a Cartesian Frame by a Quantum System},
  author = {Peres, Asher and Scudo, Petra F.},
  journal = {Phys. Rev. Lett.},
  volume = {87},
  issue = {16},
  pages = {167901},
  numpages = {4},
  year = {2001},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.87.167901},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.87.167901},
  comment = {Cited by Islam for being important in two-party reference frames.}
}

@article{PhysRevLett.91.217905,
  title = {Quantum Communication Complexity of Establishing a Shared Reference Frame},
  author = {Rudolph, Terry and Grover, Lov},
  journal = {Phys. Rev. Lett.},
  volume = {91},
  issue = {21},
  pages = {217905},
  numpages = {4},
  year = {2003},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.91.217905},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.91.217905},
  comment = {Important clock sync, but not the paper discussing Eddington, which was that?}
}

n.b.: this one has been criticized as being infeasible:
@article{chuang2000qclk,
  title={Quantum Algorithm for Distributed Clock Synchronization},
  author={Chuang, I.L.},
  journal={Physical Review Letters},
  volume={85},
  number={9},
  pages={2006--2009},
  year={2000},
  publisher={APS}
}

                  
@article{PhysRevA.72.042301,
  title = {Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement},
  author = {de{ }Burgh, Mark and Bartlett, Stephen D.},
  journal = {Phys. Rev. A},
  volume = {72},
  issue = {4},
  pages = {042301},
  numpages = {9},
  year = {2005},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.72.042301},
  url = {http://link.aps.org/doi/10.1103/PhysRevA.72.042301},
  comment = {This is the Eddington/Einstein paper.}
}

@article{giovannetti2001quantum,
  title={Quantum-enhanced positioning and clock synchronization},
  author={Giovannetti, Vittorio and Lloyd, Seth and Maccone, Lorenzo},
  journal={Nature},
  volume={412},
  number={6845},
  pages={417--419},
  year={2001},
  publisher={Nature Publishing Group}
}

@article{hwang2002eqc,
  title={Entangled quantum clocks for measuring proper-time difference},
  author={Hwang, WY and Ahn, D. and Hwang, SW and Han, YD},
  journal={The European Physical Journal D-Atomic, Molecular and Optical Physics},
  volume={19},
  number={1},
  pages={129--132},
  year={2002},
  publisher={Springer}
}

n.b.: this one was later found to have a bug, which has recently been corrected:

@article{jozsa2000qcs,
  title={Quantum Clock Synchronization Based on Shared Prior Entanglement},
  author={Jozsa, R. and Abrams, D.S. and Dowling, J.P. and Williams, C.P.},
  journal={Physical Review Letters},
  volume={85},
  number={9},
  pages={2010--2013},
  year={2000},
  doi = {10.1103/PhysRevLett.85.2010},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.85.2010},
  publisher={APS}
}

the bug report:
@article{PhysRevLett.87.129801,
  title = {Comment on "Quantum Clock Synchronization Based on Shared Prior Entanglement"},
  author = {Burt, Eric A. and Ekstrom, Christopher R. and Swanson, Thomas B.},
  journal = {Phys. Rev. Lett.},
  volume = {87},
  issue = {12},
  pages = {129801},
  numpages = {1},
  year = {2001},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.87.129801},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.87.129801}
}

first reply:
@article{PhysRevLett.87.129802,
  title = {Jozsa \emph{et al.} Reply:},
  author = {Jozsa, Richard and Abrams, Danial S. and Dowling, Jonathan P. and Williams, Colin P.},
  journal = {Phys. Rev. Lett.},
  volume = {87},
  issue = {12},
  pages = {129802},
  numpages = {1},
  year = {2001},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.87.129802},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.87.129802}
}

the bugfix, almost two decades later:
https://www.nature.com/articles/s41534-018-0090-2 <https://www.nature.com/articles/s41534-018-0090-2>
@article{ilo2018remote,
  title={Remote quantum clock synchronization without synchronized clocks},
  author={Ilo-Okeke, Ebubechukwu O and Tessler, Louis and Dowling, Jonathan P and Byrnes, Tim},
  journal={npj Quantum Information},
  volume={4},
  number={1},
  pages={1--5},
  year={2018},
  publisher={Nature Publishing Group}
}
also available in an open access preprint as arXiv:1310.6045 [quant-ph]
@article{komar14:_clock_qnet,
  author = 	 {P. K{\'o}m{\'a}r and E.M. Kessler and M. Bishof and L. Jiang and A. S. S{\/o}rensen and M. D. Lukin},
  title = 	 {A quantum network of clocks},
  journal = {Nature Physics},
  year = 	 2014,
  month = 	 jun,
  doi = {10.1038/NPHYS3000}
}

this one I don’t recall reading, but it’s in my database:
@article {Yang20170773,
	author = {Yang, Yuxiang and Chiribella, Giulio and Hayashi, Masahito},
	title = {Quantum stopwatch: how to store time in a quantum memory},
	volume = {474},
	number = {2213},
	year = {2018},
	doi = {10.1098/rspa.2017.0773},
	publisher = {The Royal Society},
	abstract = {Quantum mechanics imposes a fundamental trade-off between the accuracy of time measurements and the size of the systems used as clocks. When the measurements of different time intervals are combined, the errors due to the finite clock size accumulate, resulting in an overall inaccuracy that grows with the complexity of the set-up. Here, we introduce a method that, in principle, eludes the accumulation of errors by coherently transferring information from a quantum clock to a quantum memory of the smallest possible size. Our method could be used to measure the total duration of a sequence of events with enhanced accuracy, and to reduce the amount of quantum communication needed to stabilize clocks in a quantum network.},
	issn = {1364-5021},
	URL = {http://rspa.royalsocietypublishing.org/content/474/2213/20170773},
	eprint = {http://rspa.royalsocietypublishing.org/content/474/2213/20170773.full.pdf},
	journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}


@article{PhysRevLett.109.070503,
  title = {Longer-Baseline Telescopes Using Quantum Repeaters},
  author = {Gottesman, Daniel and Jennewein, Thomas and Croke, Sarah},
  journal = {Phys. Rev. Lett.},
  volume = {109},
  issue = {7},
  pages = {070503},
  numpages = {5},
  year = {2012},
  month = {Aug},
  doi = {10.1103/PhysRevLett.109.070503},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.109.070503},
  publisher = {American Physical Society},
  comment={n.b.: More on required performance in the journal paper,
                  but more on the derivation of the required line
                  width in the arXiv version.  The SOM includes some
                  of the derivation of numbers in the paper, and more
                  comparison against classical interferometric
                  techniques.}
}

@article{Yang:thermal15,
author = {Song Yang and XuBo Zou and GuangCan Guo and NingJuan Ruan and XuLing Lin and ZhiQiang Wu}, 
journal = {J. Opt. Soc. Am. B}, 
keywords = {Quantum optics; Quantum communications ; Quantum information and processing},
number = {6}, 
pages = {1031--1037}, 
publisher = {OSA},
title = {Long baseline weak-thermal-light interferometry with noiseless linear amplification}, 
volume = {32}, 
month = {Jun},
year = {2015},
url = {http://josab.osa.org/abstract.cfm?URI=josab-32-6-1031},
doi = {10.1364/JOSAB.32.001031},
abstract = {Long baseline weak-thermal-light interferometry is widely
                  used for retrieving astronomical information from an
                  array of telescopes. However, optic loss in the
                  baseline severely limits the length of baseline and
                  thus limits the resolution of interferometers. In
                  this paper, we consider the elimination of optic
                  loss with quantum noiseless linear amplification
                  (NLA). With a success probability of 1.98e-3, one
                  could implement a 100km long baseline interferometry
                  via 1550nm quantum communication. This shows the
                  power quantum information technique and its
                  application in astronomic interferometry. Finally,
                  the comparison with recent entanglement-assisted
                  method is also investigated.},
  comment = {Related to Gottesman.}
}

@article{PhysRevLett.107.270402,
  title = {Quantum Nonlocality in Weak-Thermal-Light Interferometry},
  author = {Tsang, Mankei},
  journal = {Phys. Rev. Lett.},
  volume = {107},
  issue = {27},
  pages = {270402},
  numpages = {5},
  year = {2011},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.107.270402},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.107.270402},
  comment = {Related to Gottesman?}
}


Rodney Van Meter
Professor, Faculty of Environment and Information Studies
Keio University, Japan
[e-mail]