Abstract

In general, a pair of uncorrelated Gaussian states mixed in a beam splitter (BS) produces a correlated state at the output. However, when the inputs are identical Gaussian states the output state is equal to the input, and no correlations appear, as the interference had not taken place. On the other hand, since physical phenomena do have observable effects, and the BS is there, a question arises on how to reveal the interference between the two beams. We prove theoretically and demonstrate experimentally that this is possible if at least one of the two beams is prepared in a discordant, i.e., Gaussian correlated, state with a third beam. We also apply the same technique to reveal the erasure of polarization information. Our experiment involves thermal states and the results show that Gaussian discordant states, even when they show a positive Glauber P-function, may be useful to achieve specific tasks.

© 2013 Optical Society of America

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References

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  1. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
    [CrossRef]
  2. D. Girolami and G. Adesso, Phys. Rev. Lett. 108, 150403 (2012).
    [CrossRef]
  3. D. Girolami and G. Adesso, Int. J. Quantum. Inform. 9, 1773 (2011).
    [CrossRef]
  4. A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
    [CrossRef]
  5. A. Ferraro and M. Paris, Phys. Rev. Lett. 108, 260403 (2012).
    [CrossRef]
  6. W. Vogel, Phys. Rev. Lett. 100, 013605 (2008).
    [CrossRef]
  7. C. Gehrke, J. Sperling, and W. Vogel, Phys. Rev. A 86, 052118 (2012).
    [CrossRef]
  8. H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
    [CrossRef]
  9. W. H. Zurek, Phys. Rev. A 67, 012320 (2003).
    [CrossRef]
  10. L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001).
    [CrossRef]
  11. P. Giorda and M. Paris, Phys. Rev. Lett. 105, 020503 (2010).
    [CrossRef]
  12. G. Adesso and A. Datta, Phys. Rev. Lett 105, 030501 (2010).
    [CrossRef]
  13. M. D. Lang, C. M. Caves, and A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011).
    [CrossRef]
  14. R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
    [CrossRef]
  15. L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
    [CrossRef]
  16. V. Madhok and A. Datta, Int. J. Mod. Phys. B 27, 1345041 (2013).
    [CrossRef]
  17. R. Glauber, Phys. Rev. 131, 2766 (1963).
    [CrossRef]
  18. E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
    [CrossRef]
  19. S. Rahimi-Keshari, C. M. Caves, and T. C. Ralph, Phys. Rev. A 87, 012119 (2013).
    [CrossRef]
  20. P. Giorda, M. Allegra, and M. G. A. Paris, Phys. Rev. A 86, 052328 (2012).
    [CrossRef]
  21. Since we are interested in correlations, we may safely assume that both the input states have zero first moments without any loss of generality.
  22. A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
    [CrossRef]
  23. S. Olivares and M. G. A. Paris, Int. J. Mod. Phys. B 27, 1345024 (2013).
    [CrossRef]
  24. S. Olivares and M. G. A. Paris, Metrologia 49, L14 (2012).
    [CrossRef]
  25. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
    [CrossRef]
  26. M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
    [CrossRef]

2013

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

V. Madhok and A. Datta, Int. J. Mod. Phys. B 27, 1345041 (2013).
[CrossRef]

S. Rahimi-Keshari, C. M. Caves, and T. C. Ralph, Phys. Rev. A 87, 012119 (2013).
[CrossRef]

S. Olivares and M. G. A. Paris, Int. J. Mod. Phys. B 27, 1345024 (2013).
[CrossRef]

2012

S. Olivares and M. G. A. Paris, Metrologia 49, L14 (2012).
[CrossRef]

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

P. Giorda, M. Allegra, and M. G. A. Paris, Phys. Rev. A 86, 052328 (2012).
[CrossRef]

A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
[CrossRef]

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
[CrossRef]

A. Ferraro and M. Paris, Phys. Rev. Lett. 108, 260403 (2012).
[CrossRef]

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

D. Girolami and G. Adesso, Phys. Rev. Lett. 108, 150403 (2012).
[CrossRef]

C. Gehrke, J. Sperling, and W. Vogel, Phys. Rev. A 86, 052118 (2012).
[CrossRef]

2011

D. Girolami and G. Adesso, Int. J. Quantum. Inform. 9, 1773 (2011).
[CrossRef]

M. D. Lang, C. M. Caves, and A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011).
[CrossRef]

2010

P. Giorda and M. Paris, Phys. Rev. Lett. 105, 020503 (2010).
[CrossRef]

G. Adesso and A. Datta, Phys. Rev. Lett 105, 030501 (2010).
[CrossRef]

2008

W. Vogel, Phys. Rev. Lett. 100, 013605 (2008).
[CrossRef]

2003

W. H. Zurek, Phys. Rev. A 67, 012320 (2003).
[CrossRef]

2002

H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
[CrossRef]

2001

L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001).
[CrossRef]

1992

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

1963

R. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
[CrossRef]

Adesso, G.

D. Girolami and G. Adesso, Phys. Rev. Lett. 108, 150403 (2012).
[CrossRef]

A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
[CrossRef]

D. Girolami and G. Adesso, Int. J. Quantum. Inform. 9, 1773 (2011).
[CrossRef]

G. Adesso and A. Datta, Phys. Rev. Lett 105, 030501 (2010).
[CrossRef]

Allegra, M.

P. Giorda, M. Allegra, and M. G. A. Paris, Phys. Rev. A 86, 052328 (2012).
[CrossRef]

Andersen, U. L.

L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
[CrossRef]

Assad, S. M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Barbieri, M.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Berni, A.

L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
[CrossRef]

Blandino, R.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Brodutch, A.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

Bruss, D.

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
[CrossRef]

Cable, H.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

Caves, C. M.

S. Rahimi-Keshari, C. M. Caves, and T. C. Ralph, Phys. Rev. A 87, 012119 (2013).
[CrossRef]

M. D. Lang, C. M. Caves, and A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011).
[CrossRef]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Chrzanowski, H. M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Datta, A.

V. Madhok and A. Datta, Int. J. Mod. Phys. B 27, 1345041 (2013).
[CrossRef]

G. Adesso and A. Datta, Phys. Rev. Lett 105, 030501 (2010).
[CrossRef]

Etesse, J.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Ferraro, A.

A. Ferraro and M. Paris, Phys. Rev. Lett. 108, 260403 (2012).
[CrossRef]

Gehrke, C.

C. Gehrke, J. Sperling, and W. Vogel, Phys. Rev. A 86, 052118 (2012).
[CrossRef]

Genoni, M. G.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Giampaolo, S. M.

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

Giorda, P.

P. Giorda, M. Allegra, and M. G. A. Paris, Phys. Rev. A 86, 052328 (2012).
[CrossRef]

P. Giorda and M. Paris, Phys. Rev. Lett. 105, 020503 (2010).
[CrossRef]

Girolami, D.

D. Girolami and G. Adesso, Phys. Rev. Lett. 108, 150403 (2012).
[CrossRef]

D. Girolami and G. Adesso, Int. J. Quantum. Inform. 9, 1773 (2011).
[CrossRef]

Glauber, R.

R. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Grangier, P.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Gu, M.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Henderson, L.

L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001).
[CrossRef]

Illuminati, F.

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

Koy Lam, P.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Lang, M. D.

M. D. Lang, C. M. Caves, and A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011).
[CrossRef]

Lassen, M.

L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
[CrossRef]

Madhok, V.

V. Madhok and A. Datta, Int. J. Mod. Phys. B 27, 1345041 (2013).
[CrossRef]

Madsen, L. S.

L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
[CrossRef]

Modi, K.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

Olivares, S.

S. Olivares and M. G. A. Paris, Int. J. Mod. Phys. B 27, 1345024 (2013).
[CrossRef]

S. Olivares and M. G. A. Paris, Metrologia 49, L14 (2012).
[CrossRef]

Ollivier, H.

H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
[CrossRef]

Paris, M.

A. Ferraro and M. Paris, Phys. Rev. Lett. 108, 260403 (2012).
[CrossRef]

P. Giorda and M. Paris, Phys. Rev. Lett. 105, 020503 (2010).
[CrossRef]

Paris, M. G. A.

S. Olivares and M. G. A. Paris, Int. J. Mod. Phys. B 27, 1345024 (2013).
[CrossRef]

S. Olivares and M. G. A. Paris, Metrologia 49, L14 (2012).
[CrossRef]

P. Giorda, M. Allegra, and M. G. A. Paris, Phys. Rev. A 86, 052328 (2012).
[CrossRef]

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Paterek, T.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

Piani, M.

A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
[CrossRef]

Rahimi-Keshari, S.

S. Rahimi-Keshari, C. M. Caves, and T. C. Ralph, Phys. Rev. A 87, 012119 (2013).
[CrossRef]

Ralph, T. C.

S. Rahimi-Keshari, C. M. Caves, and T. C. Ralph, Phys. Rev. A 87, 012119 (2013).
[CrossRef]

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Roga, W.

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

Shaji, A.

M. D. Lang, C. M. Caves, and A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011).
[CrossRef]

Sperling, J.

C. Gehrke, J. Sperling, and W. Vogel, Phys. Rev. A 86, 052118 (2012).
[CrossRef]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Streltsov, A.

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
[CrossRef]

Sudarshan, E. C. G.

E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
[CrossRef]

Symul, T.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Tualle-Brouri, R.

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

Vedral, V.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001).
[CrossRef]

Vogel, W.

C. Gehrke, J. Sperling, and W. Vogel, Phys. Rev. A 86, 052118 (2012).
[CrossRef]

W. Vogel, Phys. Rev. Lett. 100, 013605 (2008).
[CrossRef]

Zurek, W. H.

W. H. Zurek, Phys. Rev. A 67, 012320 (2003).
[CrossRef]

H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
[CrossRef]

Int. J. Mod. Phys. B

V. Madhok and A. Datta, Int. J. Mod. Phys. B 27, 1345041 (2013).
[CrossRef]

S. Olivares and M. G. A. Paris, Int. J. Mod. Phys. B 27, 1345024 (2013).
[CrossRef]

Int. J. Quantum. Inform.

M. D. Lang, C. M. Caves, and A. Shaji, Int. J. Quantum. Inform. 9, 1553 (2011).
[CrossRef]

D. Girolami and G. Adesso, Int. J. Quantum. Inform. 9, 1773 (2011).
[CrossRef]

J. Phys. A

L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001).
[CrossRef]

Metrologia

S. Olivares and M. G. A. Paris, Metrologia 49, L14 (2012).
[CrossRef]

Nat. Phys.

M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. Koy Lam, Nat. Phys. 8, 671 (2012).
[CrossRef]

Phys. Rev.

R. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Phys. Rev. A

W. H. Zurek, Phys. Rev. A 67, 012320 (2003).
[CrossRef]

A. Streltsov, S. M. Giampaolo, W. Roga, D. Bruss, and F. Illuminati, Phys. Rev. A 87, 012313 (2013).
[CrossRef]

C. Gehrke, J. Sperling, and W. Vogel, Phys. Rev. A 86, 052118 (2012).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

S. Rahimi-Keshari, C. M. Caves, and T. C. Ralph, Phys. Rev. A 87, 012119 (2013).
[CrossRef]

P. Giorda, M. Allegra, and M. G. A. Paris, Phys. Rev. A 86, 052328 (2012).
[CrossRef]

Phys. Rev. Lett

G. Adesso and A. Datta, Phys. Rev. Lett 105, 030501 (2010).
[CrossRef]

Phys. Rev. Lett.

P. Giorda and M. Paris, Phys. Rev. Lett. 105, 020503 (2010).
[CrossRef]

E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
[CrossRef]

R. Blandino, M. G. Genoni, J. Etesse, M. Barbieri, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Phys. Rev. Lett. 109, 180402 (2012).
[CrossRef]

L. S. Madsen, A. Berni, M. Lassen, and U. L. Andersen, Phys. Rev. Lett. 109, 030402 (2012).
[CrossRef]

H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
[CrossRef]

D. Girolami and G. Adesso, Phys. Rev. Lett. 108, 150403 (2012).
[CrossRef]

A. Ferraro and M. Paris, Phys. Rev. Lett. 108, 260403 (2012).
[CrossRef]

W. Vogel, Phys. Rev. Lett. 100, 013605 (2008).
[CrossRef]

A. Streltsov, G. Adesso, M. Piani, and D. Bruss, Phys. Rev. Lett. 109, 050503 (2012).
[CrossRef]

Rev. Mod. Phys.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
[CrossRef]

Other

Since we are interested in correlations, we may safely assume that both the input states have zero first moments without any loss of generality.

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Figures (3)

Fig. 1.
Fig. 1.

Revealing interference by continuous variable discordant states: scheme of the two experimental setups.

Fig. 2.
Fig. 2.

Correlation coefficients among the three beams before and after mixing of modes 1 and 2. The first plot (left) shows the evolution of the correlation between beams 1 and 2. The second plot (right) refers to correlations among beam 1 and 2 with beam 3.

Fig. 3.
Fig. 3.

Output correlations c1,3(out) (left) and c2,3(out) (right) as a function of the initial discord between modes 2 and 3. In both panels the red-dashed lines denote the curves for transmissivity equal to 15%, the solid blue lines are for the balanced case, and the green dot-sashed lines for transmissivity 85%.

Tables (2)

Tables Icon

Table 1. Measured Correlations between Beams h, k Before (in) and After (out) the BSa

Tables Icon

Table 2. Measured Correlations between the Beams h, k after the BS with Polarizersa at 45° and at V

Equations (1)

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

Σ123Σ123(out)=(σ(N,β)01τδ230σ(N,β)τδ231τδ23τδ23σ3).

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