Abstract

We propose photon energy qubits and schemes for photon energy entanglement characterization. Bell inequality violation for energy qubits and complete Bell state analysis are demonstrated theoretically. Photon energy superposition state detection is performed by a two-photon absorption interferometer based on electron transition path interference. The scheme can be realized at room-temperature by two-level systems and semiconductor devices.

© 2009 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  5. A. B. U’Ren, R. K. Erdmann, M. de la Cruz-Gutierrez, and I. A. Walmsley, “Generation of two-photon States with an arbitrary degree of entanglement via nonlinear crystal superlattices,” Phys. Rev. Lett. 97(22), 223602 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  35. J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96(13), 130502 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  38. M. O. Scully, B.-G. Englert, and C. J. Bednar, “Two-Photon Scheme for Detecting the Bell Basis Using Atomic Coherence,” Phys. Rev. Lett. 83(21), 4433–4436 (1999).
    [CrossRef]
  39. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
    [CrossRef]
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    [CrossRef]
  41. J. M. Fraser and H. M. van Driel, “Quantum interference control of free-carrier density in GaAs,” Phys. Rev. B 68(8), 085208 (2003).
    [CrossRef]
  42. A. Hayat, P. Ginzburg, D. Neiman, S. Rosenblum, and M. Orenstein, “Hyperentanglement source by intersubband two-photon emission from semiconductor quantum wells,” Opt. Lett. 33(11), 1168–1170 (2008).
    [CrossRef] [PubMed]

2009

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, “Proposed bell experiment with genuine energy-time entanglement,” Phys. Rev. Lett. 102(4), 040401 (2009).
[CrossRef] [PubMed]

F. Boitier, J.-B. Dherbecourt, A. Godard, and E. Rosencher, “Infrared quantum counting by nondegenerate two photon conductivity in GaAs,” Appl. Phys. Lett. 94(8), 081112 (2009).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

2008

B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008).
[CrossRef]

A. Hayat, P. Ginzburg, D. Neiman, S. Rosenblum, and M. Orenstein, “Hyperentanglement source by intersubband two-photon emission from semiconductor quantum wells,” Opt. Lett. 33(11), 1168–1170 (2008).
[CrossRef] [PubMed]

A. Hayat, P. Ginzburg, and M. Orenstein, “Infrared single-photon detection by two-photon absorption in silicon,” Phys. Rev. B 77(12), 125219 (2008).
[CrossRef]

A. Hayat, P. Ginzburg, and M. Orenstein, “Observation of Two-Photon Emission from Semiconductors,” Nat. Photonics 2(4), 238–241 (2008).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

A. Hayat, Y. Elor, E. Small, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92(18), 181110 (2008).
[CrossRef]

A. K. Jha, M. Malik, and R. W. Boyd, “Exploring energy-time entanglement using geometric phase,” Phys. Rev. Lett. 101(18), 180405 (2008).
[CrossRef] [PubMed]

2007

A. Hayat, P. Ginzburg, and M. Orenstein, “High-Rate Entanglement Source via Two-Photon Emission from Semiconductor Quantum Wells,” Phys. Rev. B 76(3), 035339 (2007).
[CrossRef]

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
[CrossRef] [PubMed]

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3(9), 632–635 (2007).
[CrossRef]

R. B. A. Adamson, L. K. Shalm, M. W. Mitchell, and A. M. Steinberg, “Multiparticle state tomography: hidden differences,” Phys. Rev. Lett. 98(4), 043601 (2007).
[CrossRef] [PubMed]

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75(6), 060305 (2007).
[CrossRef]

W. C. Hurlbut, Y.-S. Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. 32(6), 668–670 (2007).
[CrossRef] [PubMed]

2006

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96(13), 130502 (2006).
[CrossRef] [PubMed]

K. V. Bayandin and T. Martin, “Energy entanglement in normal metal–superconducting forks,” Phys. Rev. B 74(8), 085326 (2006).
[CrossRef]

I. A. Khan and J. C. Howell, “Experimental demonstration of high two-photon time-energy entanglement,” Phys. Rev. A 73(3), 031801 (2006).
[CrossRef]

L. Lanco, S. Ducci, J. P. Likforman, X. Marcadet, J. A. W. van Houwelingen, H. Zbinden, G. Leo, and V. Berger, “Semiconductor waveguide source of counterpropagating twin photons,” Phys. Rev. Lett. 97(17), 173901 (2006).
[CrossRef] [PubMed]

A. B. U’Ren, R. K. Erdmann, M. de la Cruz-Gutierrez, and I. A. Walmsley, “Generation of two-photon States with an arbitrary degree of entanglement via nonlinear crystal superlattices,” Phys. Rev. Lett. 97(22), 223602 (2006).
[CrossRef] [PubMed]

2004

S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations on the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69(5), 053801 (2004).
[CrossRef]

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. 84(16), 2974 (2004).
[CrossRef]

2003

J. M. Fraser and H. M. van Driel, “Quantum interference control of free-carrier density in GaAs,” Phys. Rev. B 68(8), 085208 (2003).
[CrossRef]

2000

E. DelRe, B. Crosignani, and P. Di Porto, “Scheme for total quantum teleportation,” Phys. Rev. Lett. 84(13), 2989–2992 (2000).
[CrossRef] [PubMed]

1999

M. O. Scully, B.-G. Englert, and C. J. Bednar, “Two-Photon Scheme for Detecting the Bell Basis Using Atomic Coherence,” Phys. Rev. Lett. 83(21), 4433–4436 (1999).
[CrossRef]

D. Meshulach and Y. Silberberg, “Coherent Quantum Control of Multiphoton Transitions by Shaped Ultrashort Optical Pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

1998

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Vlation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett. 81(17), 3563–3566 (1998).
[CrossRef]

Y. Silberberg and D. Meshulach, “Coherent Quantum Control of Two-Photon Transitions by a Femtosecond Laser Pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

1996

M. Michler, K. Mattle, H. Weinfurter, and A. Zeilinger, “Interferometric Bell-state analysis,” Phys. Rev. A 53(3), R1209–R1212 (1996).
[CrossRef] [PubMed]

1995

S. L. Braunstein and A. Mann, “Measurement of the Bell operator and quantum teleportation,” Phys. Rev. A 51(3), R1727–R1730 (1995).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

1993

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47(4), R2472–R2475 (1993).
[CrossRef] [PubMed]

1992

1990

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64(21), 2495–2498 (1990).
[CrossRef] [PubMed]

1989

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

1988

C. C. Gerry, “Two-photon Jaynes-Cummings model interacting with the squeezed vacuum,” Phys. Rev. A 37(7), 2683–2686 (1988).
[CrossRef] [PubMed]

1985

J. D. Franson, “Bell’s theorem and delayed determinism,” Phys. Rev. D Part. Fields 31(10), 2529–2532 (1985).
[CrossRef] [PubMed]

1964

J. S. Bell, “On the Einstein-Podolsky-Rosen Paradox,” Physics 1, 195 (1964).

1935

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47(10), 777–780 (1935).
[CrossRef]

Adamson, R. B. A.

R. B. A. Adamson, L. K. Shalm, M. W. Mitchell, and A. M. Steinberg, “Multiparticle state tomography: hidden differences,” Phys. Rev. Lett. 98(4), 043601 (2007).
[CrossRef] [PubMed]

Barreiro, J. T.

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75(6), 060305 (2007).
[CrossRef]

Bayandin, K. V.

K. V. Bayandin and T. Martin, “Energy entanglement in normal metal–superconducting forks,” Phys. Rev. B 74(8), 085326 (2006).
[CrossRef]

Bednar, C. J.

M. O. Scully, B.-G. Englert, and C. J. Bednar, “Two-Photon Scheme for Detecting the Bell Basis Using Atomic Coherence,” Phys. Rev. Lett. 83(21), 4433–4436 (1999).
[CrossRef]

Bell, J. S.

J. S. Bell, “On the Einstein-Podolsky-Rosen Paradox,” Physics 1, 195 (1964).

Bellini, M.

S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations on the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69(5), 053801 (2004).
[CrossRef]

Berger, V.

L. Lanco, S. Ducci, J. P. Likforman, X. Marcadet, J. A. W. van Houwelingen, H. Zbinden, G. Leo, and V. Berger, “Semiconductor waveguide source of counterpropagating twin photons,” Phys. Rev. Lett. 97(17), 173901 (2006).
[CrossRef] [PubMed]

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. 84(16), 2974 (2004).
[CrossRef]

Betz, M.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3(9), 632–635 (2007).
[CrossRef]

Beveratos, A.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96(13), 130502 (2006).
[CrossRef] [PubMed]

Boitier, F.

F. Boitier, J.-B. Dherbecourt, A. Godard, and E. Rosencher, “Infrared quantum counting by nondegenerate two photon conductivity in GaAs,” Appl. Phys. Lett. 94(8), 081112 (2009).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[CrossRef]

Boyd, R. W.

A. K. Jha, M. Malik, and R. W. Boyd, “Exploring energy-time entanglement using geometric phase,” Phys. Rev. Lett. 101(18), 180405 (2008).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and A. Mann, “Measurement of the Bell operator and quantum teleportation,” Phys. Rev. A 51(3), R1727–R1730 (1995).
[CrossRef] [PubMed]

Brendel, J.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Vlation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett. 81(17), 3563–3566 (1998).
[CrossRef]

Bristow, A. D.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3(9), 632–635 (2007).
[CrossRef]

Brunner, N.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96(13), 130502 (2006).
[CrossRef] [PubMed]

Cabello, A.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, “Proposed bell experiment with genuine energy-time entanglement,” Phys. Rev. Lett. 102(4), 040401 (2009).
[CrossRef] [PubMed]

Calligaro, M.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. 84(16), 2974 (2004).
[CrossRef]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47(4), R2472–R2475 (1993).
[CrossRef] [PubMed]

Costa, L.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3(9), 632–635 (2007).
[CrossRef]

Crosignani, B.

E. DelRe, B. Crosignani, and P. Di Porto, “Scheme for total quantum teleportation,” Phys. Rev. Lett. 84(13), 2989–2992 (2000).
[CrossRef] [PubMed]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

de la Cruz-Gutierrez, M.

A. B. U’Ren, R. K. Erdmann, M. de la Cruz-Gutierrez, and I. A. Walmsley, “Generation of two-photon States with an arbitrary degree of entanglement via nonlinear crystal superlattices,” Phys. Rev. Lett. 97(22), 223602 (2006).
[CrossRef] [PubMed]

De Martini, F.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, “Proposed bell experiment with genuine energy-time entanglement,” Phys. Rev. Lett. 102(4), 040401 (2009).
[CrossRef] [PubMed]

De Rossi, A.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. 84(16), 2974 (2004).
[CrossRef]

DelRe, E.

E. DelRe, B. Crosignani, and P. Di Porto, “Scheme for total quantum teleportation,” Phys. Rev. Lett. 84(13), 2989–2992 (2000).
[CrossRef] [PubMed]

Dherbecourt, J.-B.

F. Boitier, J.-B. Dherbecourt, A. Godard, and E. Rosencher, “Infrared quantum counting by nondegenerate two photon conductivity in GaAs,” Appl. Phys. Lett. 94(8), 081112 (2009).
[CrossRef]

Di Porto, P.

E. DelRe, B. Crosignani, and P. Di Porto, “Scheme for total quantum teleportation,” Phys. Rev. Lett. 84(13), 2989–2992 (2000).
[CrossRef] [PubMed]

Ducci, S.

L. Lanco, S. Ducci, J. P. Likforman, X. Marcadet, J. A. W. van Houwelingen, H. Zbinden, G. Leo, and V. Berger, “Semiconductor waveguide source of counterpropagating twin photons,” Phys. Rev. Lett. 97(17), 173901 (2006).
[CrossRef] [PubMed]

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. 84(16), 2974 (2004).
[CrossRef]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47(10), 777–780 (1935).
[CrossRef]

Elor, Y.

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A. Hayat, P. Ginzburg, D. Neiman, S. Rosenblum, and M. Orenstein, “Hyperentanglement source by intersubband two-photon emission from semiconductor quantum wells,” Opt. Lett. 33(11), 1168–1170 (2008).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
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A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, “Proposed bell experiment with genuine energy-time entanglement,” Phys. Rev. Lett. 102(4), 040401 (2009).
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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
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M. O. Scully, B.-G. Englert, and C. J. Bednar, “Two-Photon Scheme for Detecting the Bell Basis Using Atomic Coherence,” Phys. Rev. Lett. 83(21), 4433–4436 (1999).
[CrossRef]

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P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

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R. B. A. Adamson, L. K. Shalm, M. W. Mitchell, and A. M. Steinberg, “Multiparticle state tomography: hidden differences,” Phys. Rev. Lett. 98(4), 043601 (2007).
[CrossRef] [PubMed]

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B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008).
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[CrossRef] [PubMed]

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D. Meshulach and Y. Silberberg, “Coherent Quantum Control of Multiphoton Transitions by Shaped Ultrashort Optical Pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

Y. Silberberg and D. Meshulach, “Coherent Quantum Control of Two-Photon Transitions by a Femtosecond Laser Pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

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M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

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A. Hayat, Y. Elor, E. Small, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92(18), 181110 (2008).
[CrossRef]

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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
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L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3(9), 632–635 (2007).
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R. B. A. Adamson, L. K. Shalm, M. W. Mitchell, and A. M. Steinberg, “Multiparticle state tomography: hidden differences,” Phys. Rev. Lett. 98(4), 043601 (2007).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
[CrossRef] [PubMed]

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J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Vlation of Bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett. 81(17), 3563–3566 (1998).
[CrossRef]

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A. B. U’Ren, R. K. Erdmann, M. de la Cruz-Gutierrez, and I. A. Walmsley, “Generation of two-photon States with an arbitrary degree of entanglement via nonlinear crystal superlattices,” Phys. Rev. Lett. 97(22), 223602 (2006).
[CrossRef] [PubMed]

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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
[CrossRef] [PubMed]

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A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, “Proposed bell experiment with genuine energy-time entanglement,” Phys. Rev. Lett. 102(4), 040401 (2009).
[CrossRef] [PubMed]

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L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3(9), 632–635 (2007).
[CrossRef]

J. M. Fraser and H. M. van Driel, “Quantum interference control of free-carrier density in GaAs,” Phys. Rev. B 68(8), 085208 (2003).
[CrossRef]

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J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96(13), 130502 (2006).
[CrossRef] [PubMed]

L. Lanco, S. Ducci, J. P. Likforman, X. Marcadet, J. A. W. van Houwelingen, H. Zbinden, G. Leo, and V. Berger, “Semiconductor waveguide source of counterpropagating twin photons,” Phys. Rev. Lett. 97(17), 173901 (2006).
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Van Stryland, E. W.

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Walmsley, I. A.

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T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75(6), 060305 (2007).
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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
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T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
[CrossRef] [PubMed]

M. Michler, K. Mattle, H. Weinfurter, and A. Zeilinger, “Interferometric Bell-state analysis,” Phys. Rev. A 53(3), R1209–R1212 (1996).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Yuan, Z. L.

B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008).
[CrossRef]

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S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations on the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69(5), 053801 (2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Representation of an energy qubit on a Bloch sphere

Fig. 2
Fig. 2

Direct characterization of energy entanglement. (a) transition amplitude interference in TPA, (b) TPA interferometer realization scheme (c) semiconductor TPA interferometer implementation, (d) a parasitic TPA process of cross coupling possible in semiconductors at high electron crystal momentum.

Fig. 3
Fig. 3

Complete BSA scheme.

Equations (9)

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

Ψ = cos ( θ 2 ) | ω 2 + sin ( θ 2 ) e i φ | ω 1 = cos ( θ 2 ) | 1 ω 2 + sin ( θ 2 ) e i φ | 1 ω 1
E z = ( Δ 0 0 Δ )       E x = ( 0 Δ Δ 0 )         E y = ( 0 i Δ i Δ 0 )       E 0 = ( Δ 0 0 Δ )    
H ^ int = i g 1 [ σ + a 1 b 1 σ a 1 b 1 ] + i g 2 [ σ + a 2 b 2 σ a 2 b 2 ]
g 2 α 2 / g 1 α 1 = tan ( θ / 2 ) e i φ
| e z A e z ' B + e x A e z ' B + e z A e x ' B e x A e x ' B | 2
Ψ ± = 1 / 2 ( | 1 ω 1 U | 1 ω 2 D ± | 1 ω 2 U | 1 ω 1 D ) Φ ± = 1 / 2 ( | 1 ω 1 U | 1 ω 1 D ± | 1 ω 2 U | 1 ω 2 D )
Ψ + f 1 = 1 / 2 ( | 1 ω 1 U | 1 ω 2 U | 1 ω 1 D | 1 ω 2 D ) Ψ f 2 = 1 / 2 ( | 1 ω 1 U | 1 ω 2 D | 1 ω 1 D | 1 ω 2 U ) Φ + f 3 = 1 / 2 ( | 2 ω 1 U | 2 ω 1 D + | 2 ω 2 U | 2 ω 2 D ) Φ f 4 = 1 / 2 ( | 2 ω 1 U | 2 ω 1 D | 2 ω 2 U + | 2 ω 2 D )
    f 3 | D ^ U | f 3 = 1 / 2       f 4 | D ^ U | f 4 = 0       f 3 | D ^ D | f 3 = 1 / 2         f 4 | D ^ D | f 4 = 0
P = 1 8 [ ( 1 η 1 ) η 3 2 + ( 1 η 1 ) ( 1 η 3 ) 2 η 5 2 + ( 1 η 2 ) η 4 2 + ( 1 η 2 ) ( 1 η 4 ) 2 η 6 2 ]

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