Abstract

The measurement of correlations between different degrees of freedom is an important, but, in general, extremely difficult task in many applications of quantum mechanics. Here, we report an all-optical experimental detection and quantification of quantum correlations between the polarization and the frequency degrees of freedom of single photons by means of local operations acting only on the polarization degree of freedom. These operations only require experimental control over an easily accessible two-dimensional subsystem, despite handling strongly mixed quantum states comprised of a continuum of orthogonal frequency states. Our experiment thus represents a photonic realization of a scheme for the local detection of quantum correlations in a truly infinite-dimensional continuous-variable system, which excludes an efficient finite-dimensional truncation.

© 2015 Optical Society of America

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References

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  35. G. Sallen, A. Tribu, T. Aichele, R. André, L. Besombes, C. Bougerol, M. Richard, S. Tatarenko, K. Kheng, and J.-P. Poizat, “Subnanosecond spectral diffusion measurement using photon correlation,” Nat. Photonics 4, 696–699 (2010).
    [Crossref]
  36. J. Wolters, N. Sadzak, A. W. Schell, T. Schröder, and O. Benson, “Measurement of the ultrafast spectral diffusion of the optical transition of nitrogen vacancy centers in nano-size diamond using correlation interferometry,” Phys. Rev. Lett. 110, 027401 (2013).
    [Crossref]
  37. D. Girolami and G. Adesso, “Observable measure of bipartite quantum correlations,” Phys. Rev. Lett. 108, 150403 (2012).
    [Crossref]
  38. I. A. Silva, D. Girolami, R. Auccaise, R. S. Sarthour, I. S. Oliveira, T. J. Bonagamba, E. R. de Azevedo, D. O. Soares-Pinto, and G. Adesso, “Measuring bipartite quantum correlations of an unknown state,” Phys. Rev. Lett. 110, 140501 (2013).
    [Crossref]
  39. F. M. Paula, I. A. Silva, J. D. Montealegre, A. M. Souza, E. R. de Azevedo, R. S. Sarthour, A. Saguia, I. S. Oliveira, D. O. Soares-Pinto, G. Adesso, and M. S. Sarandy, “Observation of environment-induced double sudden transitions in geometric quantum correlations,” Phys. Rev. Lett. 111, 250401 (2013).
    [Crossref]

2015 (2)

M. Ringbauer, C. J. Wood, K. Modi, A. Gilchrist, A. G. White, and A. Fedrizzi, “Characterizing quantum dynamics with initial system-environment correlations,” Phys. Rev. Lett. 114, 090402 (2015).
[Crossref]

A. Orieux, M. A. Ciampini, P. Mataloni, D. Bruß, M. Rossi, and C. Macchiavello, “Experimental generation of robust entanglement from classical correlations via local dissipation,” Phys. Rev. Lett. 115, 160503 (2015).
[Crossref]

2014 (3)

G. Adesso, V. D’Ambrosio, E. Nagali, M. Piani, and F. Sciarrino, “Experimental entanglement activation from discord in a programmable quantum measurement,” Phys. Rev. Lett. 112, 140501 (2014).
[Crossref]

S. Cialdi, A. Smirne, M. G. A. Paris, S. Olivares, and B. Vacchini, “Two-step procedure to discriminate discordant from classical correlated or factorized states,” Phys. Rev. A 90, 050301(R) (2014).
[Crossref]

M. Gessner, M. Ramm, H. Häffner, A. Buchleitner, and H.-P. Breuer, “Observing a quantum phase transition by measuring a single spin,” Europhys. Lett. 107, 40005 (2014).
[Crossref]

2013 (8)

M. Gessner, M. Ramm, T. Pruttivarasin, A. Buchleitner, H.-P. Breuer, and H. Häffner, “Local detection of quantum correlations with a single trapped ion,” Nat. Phys. 10, 105–109 (2013).
[Crossref]

B. Aaronson, R. L. Franco, G. Compagno, and G. Adesso, “Hierarchy and dynamics of trace distance correlations,” New J. Phys. 15, 093022 (2013).
[Crossref]

M. Gessner and H.-P. Breuer, “Local witness for bipartite quantum discord,” Phys. Rev. A 87, 042107 (2013).
[Crossref]

J. Wolters, N. Sadzak, A. W. Schell, T. Schröder, and O. Benson, “Measurement of the ultrafast spectral diffusion of the optical transition of nitrogen vacancy centers in nano-size diamond using correlation interferometry,” Phys. Rev. Lett. 110, 027401 (2013).
[Crossref]

I. A. Silva, D. Girolami, R. Auccaise, R. S. Sarthour, I. S. Oliveira, T. J. Bonagamba, E. R. de Azevedo, D. O. Soares-Pinto, and G. Adesso, “Measuring bipartite quantum correlations of an unknown state,” Phys. Rev. Lett. 110, 140501 (2013).
[Crossref]

F. M. Paula, I. A. Silva, J. D. Montealegre, A. M. Souza, E. R. de Azevedo, R. S. Sarthour, A. Saguia, I. S. Oliveira, D. O. Soares-Pinto, G. Adesso, and M. S. Sarandy, “Observation of environment-induced double sudden transitions in geometric quantum correlations,” Phys. Rev. Lett. 111, 250401 (2013).
[Crossref]

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

R. L. Franco, B. Bellomo, S. Maniscalco, and G. Compagno, “Dynamics of quantum correlations in two-qubit systems within non-Markovian environments,” Int. J. Mod. Phys. B 27, 1345053 (2013).
[Crossref]

2012 (4)

A. Streltsov, H. Kampermann, and D. Bruß, “Quantum cost for sending entanglement,” Phys. Rev. Lett. 108, 250501 (2012).
[Crossref]

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

D. Girolami and G. Adesso, “Observable measure of bipartite quantum correlations,” Phys. Rev. Lett. 108, 150403 (2012).
[Crossref]

B. Bellomo, R. L. Franco, and G. Compagno, “Dynamics of geometric and entropic quantifiers of correlations in open quantum systems,” Phys. Rev. A 86, 012312 (2012).
[Crossref]

2011 (6)

C.-F. Li, J.-S. Tang, Y.-L. Li, and G.-C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83, 064102 (2011).
[Crossref]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system-environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[Crossref]

M. Gessner and H.-P. Breuer, “Detecting nonclassical system-environment correlations by local operations,” Phys. Rev. Lett. 107, 180402 (2011).
[Crossref]

M. Piani, S. Gharibian, G. Adesso, J. Calsamiglia, and P. Horodecki, and A. Winter, “All nonclassical correlations can be activated into distillable entanglement,” Phys. Rev. Lett. 106, 220403 (2011).
[Crossref]

M. Piani, S. Gharibian, G. Adesso, J. Calsamiglia, and P. Horodecki, and A. Winter, “All nonclassical correlations can be activated into distillable entanglement,” Phys. Rev. Lett. 106, 220403 (2011).
[Crossref]

A. Streltsov, H. Kampermann, and D. Bruß, “Linking quantum discord to entanglement in a measurement,” Phys. Rev. Lett. 106, 160401 (2011).
[Crossref]

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

2010 (3)

J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhang, X.-B. Zou, and G.-C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).

E.-M. Laine, J. Piilo, and H.-P. Breuer, “Witness for initial system-environment correlations in open-system dynamics,” Europhys. Lett. 92, 60010 (2010).
[Crossref]

G. Sallen, A. Tribu, T. Aichele, R. André, L. Besombes, C. Bougerol, M. Richard, S. Tatarenko, K. Kheng, and J.-P. Poizat, “Subnanosecond spectral diffusion measurement using photon correlation,” Nat. Photonics 4, 696–699 (2010).
[Crossref]

2008 (1)

S. Luo, “Using measurement-induced disturbance to characterize correlations as classical or quantum,” Phys. Rev. A 77, 022301 (2008).
[Crossref]

2001 (2)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref]

P. Štelmachovič and V. Bužek, “Dynamics of open quantum systems initially entangled with environment: beyond the Kraus representation,” Phys. Rev. A 64, 062106 (2001).
[Crossref]

1996 (2)

G. Lindblad, “On the existence of quantum subdynamics,” J. Phys. A 29, 4197–4207 (1996).
[Crossref]

A. Royer, “Reduced dynamics with initial correlations, and time-dependent environment and Hamiltonians,” Phys. Rev. Lett. 77, 3272–3275 (1996).
[Crossref]

1994 (2)

P. Pechukas, “Reduced dynamics need not be completely positive,” Phys. Rev. Lett. 73, 1060–1062 (1994).
[Crossref]

M. B. Ruskai, “Beyond strong subadditivity? Improved bounds on the contraction of generalized relative entropy,” Rev. Math. Phys. 6, 1147–1161 (1994).
[Crossref]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref]

1976 (1)

V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, “Completely positive semigroups of n-level systems,” J. Math. Phys. 17, 821 (1976).
[Crossref]

Aaronson, B.

B. Aaronson, R. L. Franco, G. Compagno, and G. Adesso, “Hierarchy and dynamics of trace distance correlations,” New J. Phys. 15, 093022 (2013).
[Crossref]

Adesso, G.

G. Adesso, V. D’Ambrosio, E. Nagali, M. Piani, and F. Sciarrino, “Experimental entanglement activation from discord in a programmable quantum measurement,” Phys. Rev. Lett. 112, 140501 (2014).
[Crossref]

B. Aaronson, R. L. Franco, G. Compagno, and G. Adesso, “Hierarchy and dynamics of trace distance correlations,” New J. Phys. 15, 093022 (2013).
[Crossref]

I. A. Silva, D. Girolami, R. Auccaise, R. S. Sarthour, I. S. Oliveira, T. J. Bonagamba, E. R. de Azevedo, D. O. Soares-Pinto, and G. Adesso, “Measuring bipartite quantum correlations of an unknown state,” Phys. Rev. Lett. 110, 140501 (2013).
[Crossref]

D. Girolami, T. Tufarelli, and G. Adesso, “Characterizing nonclassical correlations via local quantum uncertainty,” Phys. Rev. Lett. 110, 240402 (2013).
[Crossref]

F. M. Paula, I. A. Silva, J. D. Montealegre, A. M. Souza, E. R. de Azevedo, R. S. Sarthour, A. Saguia, I. S. Oliveira, D. O. Soares-Pinto, G. Adesso, and M. S. Sarandy, “Observation of environment-induced double sudden transitions in geometric quantum correlations,” Phys. Rev. Lett. 111, 250401 (2013).
[Crossref]

D. Girolami and G. Adesso, “Observable measure of bipartite quantum correlations,” Phys. Rev. Lett. 108, 150403 (2012).
[Crossref]

M. Piani, S. Gharibian, G. Adesso, J. Calsamiglia, and P. Horodecki, and A. Winter, “All nonclassical correlations can be activated into distillable entanglement,” Phys. Rev. Lett. 106, 220403 (2011).
[Crossref]

Aichele, T.

G. Sallen, A. Tribu, T. Aichele, R. André, L. Besombes, C. Bougerol, M. Richard, S. Tatarenko, K. Kheng, and J.-P. Poizat, “Subnanosecond spectral diffusion measurement using photon correlation,” Nat. Photonics 4, 696–699 (2010).
[Crossref]

André, R.

G. Sallen, A. Tribu, T. Aichele, R. André, L. Besombes, C. Bougerol, M. Richard, S. Tatarenko, K. Kheng, and J.-P. Poizat, “Subnanosecond spectral diffusion measurement using photon correlation,” Nat. Photonics 4, 696–699 (2010).
[Crossref]

Auccaise, R.

I. A. Silva, D. Girolami, R. Auccaise, R. S. Sarthour, I. S. Oliveira, T. J. Bonagamba, E. R. de Azevedo, D. O. Soares-Pinto, and G. Adesso, “Measuring bipartite quantum correlations of an unknown state,” Phys. Rev. Lett. 110, 140501 (2013).
[Crossref]

Bellomo, B.

R. L. Franco, B. Bellomo, S. Maniscalco, and G. Compagno, “Dynamics of quantum correlations in two-qubit systems within non-Markovian environments,” Int. J. Mod. Phys. B 27, 1345053 (2013).
[Crossref]

B. Bellomo, R. L. Franco, and G. Compagno, “Dynamics of geometric and entropic quantifiers of correlations in open quantum systems,” Phys. Rev. A 86, 012312 (2012).
[Crossref]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

Benson, O.

J. Wolters, N. Sadzak, A. W. Schell, T. Schröder, and O. Benson, “Measurement of the ultrafast spectral diffusion of the optical transition of nitrogen vacancy centers in nano-size diamond using correlation interferometry,” Phys. Rev. Lett. 110, 027401 (2013).
[Crossref]

Besombes, L.

G. Sallen, A. Tribu, T. Aichele, R. André, L. Besombes, C. Bougerol, M. Richard, S. Tatarenko, K. Kheng, and J.-P. Poizat, “Subnanosecond spectral diffusion measurement using photon correlation,” Nat. Photonics 4, 696–699 (2010).
[Crossref]

Bonagamba, T. J.

I. A. Silva, D. Girolami, R. Auccaise, R. S. Sarthour, I. S. Oliveira, T. J. Bonagamba, E. R. de Azevedo, D. O. Soares-Pinto, and G. Adesso, “Measuring bipartite quantum correlations of an unknown state,” Phys. Rev. Lett. 110, 140501 (2013).
[Crossref]

Bougerol, C.

G. Sallen, A. Tribu, T. Aichele, R. André, L. Besombes, C. Bougerol, M. Richard, S. Tatarenko, K. Kheng, and J.-P. Poizat, “Subnanosecond spectral diffusion measurement using photon correlation,” Nat. Photonics 4, 696–699 (2010).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

Breuer, H.-P.

M. Gessner, M. Ramm, H. Häffner, A. Buchleitner, and H.-P. Breuer, “Observing a quantum phase transition by measuring a single spin,” Europhys. Lett. 107, 40005 (2014).
[Crossref]

M. Gessner, M. Ramm, T. Pruttivarasin, A. Buchleitner, H.-P. Breuer, and H. Häffner, “Local detection of quantum correlations with a single trapped ion,” Nat. Phys. 10, 105–109 (2013).
[Crossref]

M. Gessner and H.-P. Breuer, “Local witness for bipartite quantum discord,” Phys. Rev. A 87, 042107 (2013).
[Crossref]

M. Gessner and H.-P. Breuer, “Detecting nonclassical system-environment correlations by local operations,” Phys. Rev. Lett. 107, 180402 (2011).
[Crossref]

E.-M. Laine, J. Piilo, and H.-P. Breuer, “Witness for initial system-environment correlations in open-system dynamics,” Europhys. Lett. 92, 60010 (2010).
[Crossref]

H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, “Non-Markovian dynamics in open quantum systems,” arXiv:1505.01385 (2015).

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2007).

Brivio, D.

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system-environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[Crossref]

Brodutch, A.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

Bruß, D.

A. Orieux, M. A. Ciampini, P. Mataloni, D. Bruß, M. Rossi, and C. Macchiavello, “Experimental generation of robust entanglement from classical correlations via local dissipation,” Phys. Rev. Lett. 115, 160503 (2015).
[Crossref]

A. Streltsov, H. Kampermann, and D. Bruß, “Quantum cost for sending entanglement,” Phys. Rev. Lett. 108, 250501 (2012).
[Crossref]

A. Streltsov, H. Kampermann, and D. Bruß, “Linking quantum discord to entanglement in a measurement,” Phys. Rev. Lett. 106, 160401 (2011).
[Crossref]

Buchleitner, A.

M. Gessner, M. Ramm, H. Häffner, A. Buchleitner, and H.-P. Breuer, “Observing a quantum phase transition by measuring a single spin,” Europhys. Lett. 107, 40005 (2014).
[Crossref]

M. Gessner, M. Ramm, T. Pruttivarasin, A. Buchleitner, H.-P. Breuer, and H. Häffner, “Local detection of quantum correlations with a single trapped ion,” Nat. Phys. 10, 105–109 (2013).
[Crossref]

Bužek, V.

P. Štelmachovič and V. Bužek, “Dynamics of open quantum systems initially entangled with environment: beyond the Kraus representation,” Phys. Rev. A 64, 062106 (2001).
[Crossref]

Cable, H.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: discord and related measures,” Rev. Mod. Phys. 84, 1655–1707 (2012).
[Crossref]

K. Modi, H. Cable, M. Williamson, and V. Vedral, “Quantum correlations in mixed-state metrology,” Phys. Rev. X 1, 021022 (2011).

Calsamiglia, J.

M. Piani, S. Gharibian, G. Adesso, J. Calsamiglia, and P. Horodecki, and A. Winter, “All nonclassical correlations can be activated into distillable entanglement,” Phys. Rev. Lett. 106, 220403 (2011).
[Crossref]

Cialdi, S.

S. Cialdi, A. Smirne, M. G. A. Paris, S. Olivares, and B. Vacchini, “Two-step procedure to discriminate discordant from classical correlated or factorized states,” Phys. Rev. A 90, 050301(R) (2014).
[Crossref]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system-environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[Crossref]

Ciampini, M. A.

A. Orieux, M. A. Ciampini, P. Mataloni, D. Bruß, M. Rossi, and C. Macchiavello, “Experimental generation of robust entanglement from classical correlations via local dissipation,” Phys. Rev. Lett. 115, 160503 (2015).
[Crossref]

Cirac, J. I.

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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. System is realized by the polarization state and the frequency modes of single photons. Alice generates and filters out the single photons, then sends the photons to a polarizer followed by a calcite crystal, realizing a quantum channel, and finally to a random-number-generator (RNG) driven half-wave plate (HWP0) to prepare the initial state ρ S E , which is sent to Bob. Bob measures the quantum correlation of the initial state using local operations on the polarization state. His setup consists of four sections: (1) three removable mirrors (RM1, RM2, RM3) direct the photons to different functional modules; (2) a computer-controlled half-wave plate (HWP1) and a long PM fiber constitute the controlled dephasing map in which the state ρ S E is created; (3) a Michelson delay setup including HWP2, PBS1, QWP1, QWP2, M1, and M2 generate unitary evolutions; and (4) T1 and T2 are two tomography sets on the polarization subsystem.
Fig. 2.
Fig. 2. Visibility of single photons in the Michelson interferometer (a) without and (b) with a calcite, where x is the delay between the two arms. After a Fourier transformation, the data will show the frequency spectrum of the single photons. The red lines show fits based on a Lorentzian spectrum. The shift of the zero point in (b) can be used to calculate the birefringence of the calcite.
Fig. 3.
Fig. 3. Experimental results for the local trace distance Δ ( η , x ) , with x = c τ / 2 for different η -values [from (a) to (h): η = n π / 16 with n = 0 7 ] and an initial state prepared with t = L Δ n cal / c and L = 35.92 mm . The black lines show the theoretical prediction according to Eq. (9).
Fig. 4.
Fig. 4. Experimental results of the local detection scheme to measure initial quantum correlations (black dots and error bars). The red line shows the theoretical prediction given by Eq. (10), while the blue line represents the quantum correlations of the initial state according to Eq. (7). L is the length of the calcite crystal, which can be considered as the different positions in a quantum channel.

Equations (10)

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ρ S E ρ S E = μ Π μ ρ S E Π μ ,
δ ( ρ S E ) = ρ S E ρ S E ,
Δ ( τ ) = ρ S ( τ ) ρ S ( τ )
Δ ( τ ) δ ( ρ S E ) .
max τ Δ ( τ ) δ ( ρ S E ) .
G ( ω ) = δ ω π 1 δ ω 2 + ( ω ω 0 ) 2 ,
δ ( ρ S E ) = 1 2 d ω G ( ω ) | e i ( ω ω 0 ) t e i ( ω ω 0 ) t | ,
Δ ( τ ) = 1 2 | d ω G ( ω ) ( e i ( ω ω 0 ) t e i ( ω ω 0 ) t ) e i ω τ | .
Δ ( τ ) = 1 2 | e δ ω | t + τ | e δ ω | t τ | | ,
max τ Δ ( τ ) = 1 2 ( 1 e 2 δ ω t ) ,

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