Abstract

We show how to convert between partially coherent superpositions of a single photon with the vacuum by using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input, can improve the generalized efficiency.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. P. Lund and T. C. Ralph, Phys. Rev. A 66, 032307 (2002).
    [CrossRef]
  2. T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B Quantum Semiclass. Opt. 7, S245 (2005).
    [CrossRef]
  3. A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
    [CrossRef] [PubMed]
  4. D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett. 81, 1604 (1998).
    [CrossRef]
  5. S. A. Babichev, J. Ries, and A. I. Lvovsky, Europhys. Lett. 64, 1 (2003).
    [CrossRef]
  6. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
    [CrossRef] [PubMed]
  7. S. A. Babichev, B. Brezger, and A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004).
    [CrossRef] [PubMed]
  8. A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
    [CrossRef] [PubMed]
  9. D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
    [CrossRef]
  10. D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
    [CrossRef]

2005 (1)

T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B Quantum Semiclass. Opt. 7, S245 (2005).
[CrossRef]

2004 (3)

S. A. Babichev, B. Brezger, and A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
[CrossRef]

2003 (1)

S. A. Babichev, J. Ries, and A. I. Lvovsky, Europhys. Lett. 64, 1 (2003).
[CrossRef]

2002 (2)

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

A. P. Lund and T. C. Ralph, Phys. Rev. A 66, 032307 (2002).
[CrossRef]

2001 (1)

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

1998 (1)

D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett. 81, 1604 (1998).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Aichele, T.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Babichev, S. A.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

S. A. Babichev, J. Ries, and A. I. Lvovsky, Europhys. Lett. 64, 1 (2003).
[CrossRef]

Barnett, S. M.

D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett. 81, 1604 (1998).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Benson, O.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Berry, D. W.

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Brezger, B.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Hansen, H.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Knight, P. L.

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
[CrossRef]

Laflamme, R.

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

Lund, A. P.

T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B Quantum Semiclass. Opt. 7, S245 (2005).
[CrossRef]

A. P. Lund and T. C. Ralph, Phys. Rev. A 66, 032307 (2002).
[CrossRef]

Lvovsky, A. I.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

S. A. Babichev, J. Ries, and A. I. Lvovsky, Europhys. Lett. 64, 1 (2003).
[CrossRef]

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Mlynek, J.

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Myers, C. R.

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

Pegg, D. T.

D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett. 81, 1604 (1998).
[CrossRef]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Phillips, L. S.

D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett. 81, 1604 (1998).
[CrossRef]

Ralph, T. C.

T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B Quantum Semiclass. Opt. 7, S245 (2005).
[CrossRef]

A. P. Lund and T. C. Ralph, Phys. Rev. A 66, 032307 (2002).
[CrossRef]

Ries, J.

S. A. Babichev, J. Ries, and A. I. Lvovsky, Europhys. Lett. 64, 1 (2003).
[CrossRef]

Sanders, B. C.

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
[CrossRef]

Scheel, S.

D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
[CrossRef]

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

Schiller, S.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Wiseman, H. M.

T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B Quantum Semiclass. Opt. 7, S245 (2005).
[CrossRef]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Europhys. Lett. (1)

S. A. Babichev, J. Ries, and A. I. Lvovsky, Europhys. Lett. 64, 1 (2003).
[CrossRef]

J. Opt. B Quantum Semiclass. Opt. (1)

T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B Quantum Semiclass. Opt. 7, S245 (2005).
[CrossRef]

New J. Phys. (1)

D. W. Berry, S. Scheel, C. R. Myers, B. C. Sanders, P. L. Knight, and R. Laflamme, New J. Phys. 6, 93 (2004).
[CrossRef]

Phys. Rev. A (2)

D. W. Berry, S. Scheel, B. C. Sanders, and P. L. Knight, Phys. Rev. A 69, 031806 (2004).
[CrossRef]

A. P. Lund and T. C. Ralph, Phys. Rev. A 66, 032307 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
[CrossRef] [PubMed]

D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett. 81, 1604 (1998).
[CrossRef]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

S. A. Babichev, B. Brezger, and A. I. Lvovsky, Phys. Rev. Lett. 92, 047903 (2004).
[CrossRef] [PubMed]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, Phys. Rev. Lett. 87, 050402 (2001).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

General scheme for converting one mixed state of zero and one photon to another.

Fig. 2
Fig. 2

(a) General setup for transforming the state ρ ̂ to ρ ̂ , involving an interferometer and a conditional measurement. (b) Same interferometer after absorbing all but a line of beam splitters into the measurement.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ρ ̂ = E ψ ψ + ( 1 E ) 0 0 ,
ρ ̂ = E [ ( α θ 0 + β r θ 1 ) 0 + β t θ 0 1 ] H . c . + ( 1 E ) θ 0 2 0 0 ,
β ( α θ 0 + β r θ 1 ) = α β t θ 0 .
Tr [ ρ ̂ ] = E ( α θ 0 + β r θ 1 2 + β t θ 0 2 ) + ( 1 E ) θ 0 2 ,
E = E ( α θ 0 + β r θ 1 2 + β t θ 0 2 ) Tr [ ρ ̂ ] .
t β E ( 1 E ) = β E ( 1 E ) ,
p success Tr [ ρ ̂ ] = θ 0 2 ( 1 E ) ( 1 E ) .
E ( ρ ̂ ) ρ 11 1 ρ 01 2 ρ 11 = β 2 E 1 α 2 E ,
E [ p ρ ̂ 1 + ( 1 p ) ρ ̂ 2 ] p E ( ρ ̂ 1 ) + ( 1 p ) E ( ρ ̂ 2 ) ,
E [ p ρ ̂ 1 + ( 1 p ) ρ ̂ 2 ] = p β 1 2 E 1 1 p α 1 2 E 1 p β 1 2 E 1 1 α 1 2 E 1 = p E ( ρ ̂ 1 ) + ( 1 p ) E ( ρ ̂ 2 ) .
f ( p ) = 2 ρ 11 2 Δ ρ 10 2 ( ρ 11 ρ 10 2 ) 2 + 2 [ Δ ρ 11 ρ 10 2 ρ 11 2 Re ( ρ 01 Δ ρ 10 ) ] 2 ( ρ 11 ρ 10 2 ) 3 ,

Metrics