Abstract

Integrated optics allows for the generation and control of increasingly complex photonic states on chip-based architectures. Here, we implement two entangled qutrits—a nine-dimensional quantum system—and demonstrate an exceptionally high degree of experimental control. The approach, which is conceptually different to common bulk optical implementations, is heavily based on methods of integrated in-fiber and on-chip technologies and further motivated by methods commonly used in today’s telecommunications industry. The system is composed of an in-fiber source creating entangled qutrit states of any amplitude and phase, and an on-chip integrated general Multiport enabling the realization of any desired local unitary transformation within the two qutrit nine-dimensional Hilbert space. The complete design is readily extendible toward higher dimensions with moderate increase in complexity. Ultimately, our scheme allows for complete on-chip integration. We demonstrate the flexibility and generality of our system by realizing a complete characterization of the two-qutrit space of higher-order Einstein–Podolsky–Rosen correlations.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2013 (5)

M. Huber, J. I. de Vicente, “Structure of multidimensional entanglement in multipartite systems,” Phys. Rev. Lett. 110, 030501 (2013).
[Crossref]

M. Tillmann, B. Dakic, R. Heilmann, S. Nolte, A. Szameit, P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

M. Suda, C. Pacher, M. Peev, M. Dusek, F. Hipp, “Experimental access to higher-dimensional entangled quantum systems using integrated optics,” Quantum Inf. Process. 12, 1915–1945 (2013).

2012 (5)

Ch. Spengler, M. Huber, B. C. Hiesmayr, “Composite parameterization and Haar measure for all unitary and special unitary groups,” J. Math. Phys. 53, 013501 (2012).
[Crossref]

G. N. M. Tabia, “Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices,” Phys. Rev. A 86, 062107 (2012).
[Crossref]

C. Spengler, M. Huber, S. Brierley, T. Adaktylos, B. C. Hiesmayr, “Entanglement detection via mutually unbiased bases,” Phys. Rev. A 86, 022311 (2012).
[Crossref]

C. Schaeff, R. Polster, R. Lapkiewicz, R. Fickler, S. Ramelow, A. Zeilinger, “Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits,” Opt. Express 20, 16145–16153 (2012).
[Crossref]

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

2011 (3)

M. Wiesniak, T. Paterek, A. Zeilinger, “Entanglement in mutually unbiased bases,” New J. Phys. 13, 053047 (2011).
[Crossref]

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wiesniak, A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493, (2011).
[Crossref]

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. Thompson, J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[Crossref]

2010 (1)

A. Laing, V. Scarani, J. G. Rarity, J. L. O’Brien, “Reference-frame-independent quantum key distribution,” Phys. Rev. A 82, 012304 (2010).
[Crossref]

2009 (2)

J. C. F. Matthews, A. Politi, A. Stefanov, J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[Crossref]

A. Politi, J. C. F. Matthews, J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science 325, 1221 (2009).
[Crossref]

2007 (1)

I. Bengtsson, W. Bruzda, A. Ericsson, J.-A. Larsson, W. Tadej, K. Zyczkowski, “Mutually unbiased bases and Hadamard matrices of order six,” J. Math. Phys. 48, 052106 (2007).
[Crossref]

2006 (1)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

2005 (1)

Y. Lim, A. Beige, “Multiphoton entanglement through a Bell-multiport beam splitter,” Phys. Rev. A 71, 062311 (2005).
[Crossref]

2004 (1)

M. Mohseni, A. M. Steinberg, J. A. Bergou, “Optical realization of optimal unambiguous discrimination for pure and mixed quantum states,” Phys. Rev. Lett. 93, 200403 (2004).
[Crossref]

2002 (2)

D. Collins, N. Gisin, N. Linden, S. Massar, S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref]

D. Kaszlikowski, M. Zukowski, “Greenberger-Horne-Zeilinger paradoxes for N N-dimensional systems,” Phys. Rev. A 66, 1–6 (2002).

2001 (1)

1999 (1)

1998 (1)

N. Cerf, C. Adami, P. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[Crossref]

1997 (1)

M. Zukowski, A. Zeilinger, M. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A 55, 2564–2579 (1997).
[Crossref]

1996 (1)

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

1984 (1)

M. Haruna, J. Koyama, “Thermo-optic waveguide interferometric modulator/switch in glass,” IEE Proc, Part H 131, 322–324 (1984).
[Crossref]

1981 (1)

A. Zeilinger, “General properties of lossless beam splitters in interferometry,” Am. J. Phys. 49, 882–883 (1981).
[Crossref]

Adaktylos, T.

C. Spengler, M. Huber, S. Brierley, T. Adaktylos, B. C. Hiesmayr, “Entanglement detection via mutually unbiased bases,” Phys. Rev. A 86, 022311 (2012).
[Crossref]

Adami, C.

N. Cerf, C. Adami, P. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[Crossref]

Amselem, E.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

Barbieri, M.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Beige, A.

Y. Lim, A. Beige, “Multiphoton entanglement through a Bell-multiport beam splitter,” Phys. Rev. A 71, 062311 (2005).
[Crossref]

Bengtsson, I.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

I. Bengtsson, W. Bruzda, A. Ericsson, J.-A. Larsson, W. Tadej, K. Zyczkowski, “Mutually unbiased bases and Hadamard matrices of order six,” J. Math. Phys. 48, 052106 (2007).
[Crossref]

I. Bengtsson, “Three ways to look at mutually unbiased bases,” arXiv:quant-ph/0610216v1 (2006).

Bergou, J. A.

M. Mohseni, A. M. Steinberg, J. A. Bergou, “Optical realization of optimal unambiguous discrimination for pure and mixed quantum states,” Phys. Rev. Lett. 93, 200403 (2004).
[Crossref]

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Blanchfield, K.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

Bourennane, M.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

Brierley, S.

C. Spengler, M. Huber, S. Brierley, T. Adaktylos, B. C. Hiesmayr, “Entanglement detection via mutually unbiased bases,” Phys. Rev. A 86, 022311 (2012).
[Crossref]

Brod, D. J.

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

Broome, M. A.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Bruzda, W.

I. Bengtsson, W. Bruzda, A. Ericsson, J.-A. Larsson, W. Tadej, K. Zyczkowski, “Mutually unbiased bases and Hadamard matrices of order six,” J. Math. Phys. 48, 052106 (2007).
[Crossref]

Cabello, A.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

Cerf, N.

N. Cerf, C. Adami, P. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[Crossref]

Chaboyer, Z.

Z. Chaboyer, T. Meany, L. G. Helt, M. J. Withford, M. J. Steel, “Tuneable quantum interference in a 3D integrated circuit,” arXiv:1409.4908 (2014).

Collins, D.

D. Collins, N. Gisin, N. Linden, S. Massar, S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref]

Crespi, A.

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

Dakic, B.

M. Tillmann, B. Dakic, R. Heilmann, S. Nolte, A. Szameit, P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
[Crossref]

de Vicente, J. I.

M. Huber, J. I. de Vicente, “Structure of multidimensional entanglement in multipartite systems,” Phys. Rev. Lett. 110, 030501 (2013).
[Crossref]

Dusek, M.

M. Suda, C. Pacher, M. Peev, M. Dusek, F. Hipp, “Experimental access to higher-dimensional entangled quantum systems using integrated optics,” Quantum Inf. Process. 12, 1915–1945 (2013).

Ericsson, A.

I. Bengtsson, W. Bruzda, A. Ericsson, J.-A. Larsson, W. Tadej, K. Zyczkowski, “Mutually unbiased bases and Hadamard matrices of order six,” J. Math. Phys. 48, 052106 (2007).
[Crossref]

Fickler, R.

Galvao, E. F.

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

Gates, J. C.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Gisin, N.

D. Collins, N. Gisin, N. Linden, S. Massar, S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[Crossref]

Goh, T.

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Haruna, M.

M. Haruna, J. Koyama, “Thermo-optic waveguide interferometric modulator/switch in glass,” IEE Proc, Part H 131, 322–324 (1984).
[Crossref]

Hattori, K.

Heilmann, R.

M. Tillmann, B. Dakic, R. Heilmann, S. Nolte, A. Szameit, P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
[Crossref]

Helt, L. G.

Z. Chaboyer, T. Meany, L. G. Helt, M. J. Withford, M. J. Steel, “Tuneable quantum interference in a 3D integrated circuit,” arXiv:1409.4908 (2014).

Hibino, Y.

T. Shibata, M. Okuno, T. Goh, M. Yasu, M. Itoh, M. Ishii, Y. Hibino, A. Sugita, A. Himeno, “Silica-based 16 16 optical matrix switch module with integrated driving circuits,” in Optical Fiber Communication Conference and International Conference on Quantum Information (Optical Society of America, 2001), paper WR1.

Hiesmayr, B. C.

C. Spengler, M. Huber, S. Brierley, T. Adaktylos, B. C. Hiesmayr, “Entanglement detection via mutually unbiased bases,” Phys. Rev. A 86, 022311 (2012).
[Crossref]

Ch. Spengler, M. Huber, B. C. Hiesmayr, “Composite parameterization and Haar measure for all unitary and special unitary groups,” J. Math. Phys. 53, 013501 (2012).
[Crossref]

Himeno, A.

Hipp, F.

M. Suda, C. Pacher, M. Peev, M. Dusek, F. Hipp, “Experimental access to higher-dimensional entangled quantum systems using integrated optics,” Quantum Inf. Process. 12, 1915–1945 (2013).

Horne, M.

M. Zukowski, A. Zeilinger, M. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A 55, 2564–2579 (1997).
[Crossref]

Huber, M.

M. Huber, J. I. de Vicente, “Structure of multidimensional entanglement in multipartite systems,” Phys. Rev. Lett. 110, 030501 (2013).
[Crossref]

C. Spengler, M. Huber, S. Brierley, T. Adaktylos, B. C. Hiesmayr, “Entanglement detection via mutually unbiased bases,” Phys. Rev. A 86, 022311 (2012).
[Crossref]

Ch. Spengler, M. Huber, B. C. Hiesmayr, “Composite parameterization and Haar measure for all unitary and special unitary groups,” J. Math. Phys. 53, 013501 (2012).
[Crossref]

Humphreys, P. C.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Ishii, M.

T. Shibata, M. Okuno, T. Goh, M. Yasu, M. Itoh, M. Ishii, Y. Hibino, A. Sugita, A. Himeno, “Silica-based 16 16 optical matrix switch module with integrated driving circuits,” in Optical Fiber Communication Conference and International Conference on Quantum Information (Optical Society of America, 2001), paper WR1.

Itoh, M.

T. Shibata, M. Okuno, T. Goh, M. Yasu, M. Itoh, M. Ishii, Y. Hibino, A. Sugita, A. Himeno, “Silica-based 16 16 optical matrix switch module with integrated driving circuits,” in Optical Fiber Communication Conference and International Conference on Quantum Information (Optical Society of America, 2001), paper WR1.

S. Sohma, T. Watanabe, N. Ooba, M. Itoh, T. Shibata, H. Takahashi, “Silica-based PLC Type 32 × 32 optical matrix switch,” in European Conference on Optical Communications (ECOC) 2006 (IEEE, 2006), pp. 1–2.

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Jin, X.-M.

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Figures (4)

Fig. 1.
Fig. 1.

Concept of an entangled two-quNit N2-dimensional quantum experiment. A source (S) creates the path-encoded entangled two-quNits state. After separation, each quNit passes N1 phase shifters followed by a local unitary transformation (U). Eventually, the state is detected and coincidence detection events are recorded (D).

Fig. 2.
Fig. 2.

Illustration of the experimental arrangement. All components are directly interfaced via standard optical fiber connectors or directly spliced together for minimal optical loss. (S) A superposition between N photon pair creation events is produced by coherently pumping N nonlinear crystals. For each channel, the photon pair is separated by wavelength followed by a number of in-fiber components ensuring matching optical properties. Eventually, an entangled two-qutrit state is obtained. Using the interference signal of reference light (λ765,λ785) inserted backward into the system, a proportional integral derivative (PID) controller is actively stabilizing all phases of the in-fiber system. (U) Each qutrit is directly connected to the packaged MPs performing any arbitrary local unitary transformation onto the system. (D) Eventually, using single-photon detectors, the measurement concludes when pair-detection events are recorded.

Fig. 3.
Fig. 3.

A full scan of the two-qutrit correlation space spanned by the two relative phases CCab(ϕx,ϕy) is performed (top row) and compared to theoretical predictions (bottom row). Iteratively, ϕx is set to 0°,10°,20°,,360° in steps of 10°. For each value of ϕx, ϕy is measured in 30 steps between 0 and 2π. Eventually, a fit f(ϕy) is applied to the recorded correlation signal CCab|ϕxϕy(0,2π). The resulting 36 fitted signals f(ϕy) are displayed for each ϕx and for every detector combination {(i,I),(i,II),(i,III)} slice by slice. The maximum coincidence count rates reach approximately 600/8 s at a SNR10. The overlays of the top right picture are used to highlight special characteristics of the correlation space as described in the text. The experiment is calibrated, controlled, stabilized, and performed fully automatically.

Fig. 4.
Fig. 4.

Estimated coverage of the unitary space of an N×N MP of standard design [1,15]. Each plotted line assumes a different extinction ratio for all MZI units inside the MP. Phase shifters are assumed to cover the full range of phases, as has been experimentally verified. Currently, the characterized MP exhibits an average visibility of (96.3±0.01)% [extinction ratio of (14.2±0.1)dB]. However, the current MP implementation has the a first/prototype run. Consequently, we are confident that next-generation devices tailored toward high extinction ratios will provide significant improvements. As an example, a 10-dimensional MP with an extinction ratio of 30dB of all MZIs can realize more than 92% of the full unitary SU(10) space.

Equations (8)

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

|ψN=k=1NAkeϕkϕk|kk.
|ψN(UAUB)|ψN.
Pab=|aa||bb|,
|ψN=k=1NAkeϕkϕk|kk.
UA/B=((a/b)11(a/b)12(a/b)13(a/b)12(a/b)22eϕ22(a/b)23eϕ23(a/b)13(a/b)23eϕ23(a/b)33eϕ33),
U=13(1111e2π3eπ31e2π3e2π3)(1111e2π3eπ31e2π3e2π3).
S¯=(0.703±0.019)rad1.
covN=i=1N2minλimaxλidλiJNU(N)dUN,

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