Abstract

A classical optics setup to simulate the quantum teleportation process is presented. The analogy is based on the possibility of encoding a quantum state of a system with a 2N-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a basis is associated with the complex amplitude of the electromagnetic field in a given region of the laser wavefront. Temporal evolutions are represented as changes of the complex amplitude of the field when the wavefront is modified by different optical elements. The classical optics representation of quantum state as images and of universal quantum gates as optical processors is shown. The design and operation of an optical module that is used to simulate the quantum teleportation process are discussed. Experimental results where the teleportation of a one qbit state is simulated are shown.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777-780 (1935).
    [CrossRef]
  2. 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] [PubMed]
  3. D. Bouwmeester, J. M. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
    [CrossRef]
  4. D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
    [CrossRef]
  5. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706-709 (1998).
    [CrossRef] [PubMed]
  6. M. A. Nielsen, E. Knill, and R. Laflamme, “Complete quantum teleportation using nuclear magnetic resonance,” Nature 396, 52-55 (1998).
    [CrossRef]
  7. R. J. C. Spreeuw, “Classical analogy of entanglement,” Found. Phys. 28, 361-374 (1998).
    [CrossRef]
  8. R. J. C. Spreeuw, “Classical wave-optics analogy of quantum information processing,” Phys. Rev. A 63, 062302 (2001).
    [CrossRef]
  9. N. Bhattacharya, H. B. van Linden van den Heuvell, and R. J. C. Spreeuw, “Implementation of quantum search algorithm using classical Fourier optics,” Phys. Rev. Lett. 88, 137901 (2002).
    [CrossRef] [PubMed]
  10. G. Puentes, C. La Mela, S. Ledesma, C. Iemmi, J. P. Paz, and M. Saraceno, “Optical simulation of quantum algorithms using programmable liquid crystal displays,” Phys. Rev. A 69, 042319 (2004).
    [CrossRef]
  11. D. Francisco, C. Iemmi, J. P. Paz, and S. Ledesma, “Optical simulation of the quantum Hadamard operator,” Opt. Commun. 268, 340-345 (2006).
    [CrossRef]
  12. N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477-R1480 (1998).
    [CrossRef]
  13. D. Francisco, C. Iemmi, J. P. Paz, and S. Ledesma, “Simulating a quantum walk with classical optics,” Phys. Rev. A 74, 052327 (2006).
    [CrossRef]
  14. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge U. Press, 1987).
  15. R. Blume-Kohout, C. M. Caves, and I. H. Deutsch, “Physical-resource requirements and the power of quantum computation,” Found. Phys. 32, 1641-1670 (2002).
    [CrossRef]
  16. M. Nielsen and I. Chuang, Quantum Information and Computation (Cambridge U. Press, 2000).
  17. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. (Bellingham) 40, 2558-2564 (2001).
    [CrossRef]

2006 (2)

D. Francisco, C. Iemmi, J. P. Paz, and S. Ledesma, “Optical simulation of the quantum Hadamard operator,” Opt. Commun. 268, 340-345 (2006).
[CrossRef]

D. Francisco, C. Iemmi, J. P. Paz, and S. Ledesma, “Simulating a quantum walk with classical optics,” Phys. Rev. A 74, 052327 (2006).
[CrossRef]

2004 (1)

G. Puentes, C. La Mela, S. Ledesma, C. Iemmi, J. P. Paz, and M. Saraceno, “Optical simulation of quantum algorithms using programmable liquid crystal displays,” Phys. Rev. A 69, 042319 (2004).
[CrossRef]

2002 (2)

N. Bhattacharya, H. B. van Linden van den Heuvell, and R. J. C. Spreeuw, “Implementation of quantum search algorithm using classical Fourier optics,” Phys. Rev. Lett. 88, 137901 (2002).
[CrossRef] [PubMed]

R. Blume-Kohout, C. M. Caves, and I. H. Deutsch, “Physical-resource requirements and the power of quantum computation,” Found. Phys. 32, 1641-1670 (2002).
[CrossRef]

2001 (2)

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. (Bellingham) 40, 2558-2564 (2001).
[CrossRef]

R. J. C. Spreeuw, “Classical wave-optics analogy of quantum information processing,” Phys. Rev. A 63, 062302 (2001).
[CrossRef]

1998 (5)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706-709 (1998).
[CrossRef] [PubMed]

M. A. Nielsen, E. Knill, and R. Laflamme, “Complete quantum teleportation using nuclear magnetic resonance,” Nature 396, 52-55 (1998).
[CrossRef]

R. J. C. Spreeuw, “Classical analogy of entanglement,” Found. Phys. 28, 361-374 (1998).
[CrossRef]

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477-R1480 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J. M. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[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] [PubMed]

1935 (1)

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

Found. Phys. (2)

R. J. C. Spreeuw, “Classical analogy of entanglement,” Found. Phys. 28, 361-374 (1998).
[CrossRef]

R. Blume-Kohout, C. M. Caves, and I. H. Deutsch, “Physical-resource requirements and the power of quantum computation,” Found. Phys. 32, 1641-1670 (2002).
[CrossRef]

Nature (2)

M. A. Nielsen, E. Knill, and R. Laflamme, “Complete quantum teleportation using nuclear magnetic resonance,” Nature 396, 52-55 (1998).
[CrossRef]

D. Bouwmeester, J. M. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

Opt. Commun. (1)

D. Francisco, C. Iemmi, J. P. Paz, and S. Ledesma, “Optical simulation of the quantum Hadamard operator,” Opt. Commun. 268, 340-345 (2006).
[CrossRef]

Opt. Eng. (Bellingham) (1)

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. (Bellingham) 40, 2558-2564 (2001).
[CrossRef]

Phys. Rev. (1)

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

Phys. Rev. A (4)

G. Puentes, C. La Mela, S. Ledesma, C. Iemmi, J. P. Paz, and M. Saraceno, “Optical simulation of quantum algorithms using programmable liquid crystal displays,” Phys. Rev. A 69, 042319 (2004).
[CrossRef]

R. J. C. Spreeuw, “Classical wave-optics analogy of quantum information processing,” Phys. Rev. A 63, 062302 (2001).
[CrossRef]

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477-R1480 (1998).
[CrossRef]

D. Francisco, C. Iemmi, J. P. Paz, and S. Ledesma, “Simulating a quantum walk with classical optics,” Phys. Rev. A 74, 052327 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

N. Bhattacharya, H. B. van Linden van den Heuvell, and R. J. C. Spreeuw, “Implementation of quantum search algorithm using classical Fourier optics,” Phys. Rev. Lett. 88, 137901 (2002).
[CrossRef] [PubMed]

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] [PubMed]

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

Science (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Other (2)

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge U. Press, 1987).

M. Nielsen and I. Chuang, Quantum Information and Computation (Cambridge U. Press, 2000).

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 (6)

Fig. 1
Fig. 1

Scheme of the quantum circuit that performs the quantum teleportation of a single qbit. The meters represent measurement, and the double line coming out of them represents classical bits while single lines denote qbits.

Fig. 2
Fig. 2

Spatial organization of the input plane in order to perform the optical representation of the N qbits state.

Fig. 3
Fig. 3

Reduced setup of the optically simulated universal quantum gates. (a) Coherent optical processor for simulating U ( 2 ) gates: The phase plates P P ( δ ) and P P ( β ) in the input and output planes perform rotations generated by the Pauli Z operator. The phase grating G ( γ ) in the Fourier plane performs rotations generated by the Pauli Y operator. (b) CP as an optical simulation of the CNOT gate.

Fig. 4
Fig. 4

Scheme of the optical setup for quantum teleportation. In Stage 1, the binary mask P 1 represents the three qbit state ϕ ( t = 0 ) . In Stage 2 a CP and an optical processor are used for performing a Bell measurement on qbits 1 and 2. In Stage 3 a computational measurement on qbits 1 and 2 is performed. In Stage 4 another optical processor is used for simulating the correcting U ( 2 ) gate on qbit 3. The unknown input state is the recovery in the state of the third qbit at the end of the process.

Fig. 5
Fig. 5

Set of unitary correcting U ( Z 1 , Z 2 ) operators in their optical setup representations. From the left to the right: U ( + + ) is the identity operator, U ( + ) is the Pauli X operator, U ( + ) is the Pauli Z operator, and finally, U ( ) is the product of Pauli X Z operators.

Fig. 6
Fig. 6

Experimental results. In (a)–(d) we show the temporal evolution of the global three qbit state before Alice’s measurement. In (e1)–(e4) we show the recovery unknown state in the third qbit after Bob’s correction for each possible result of Alice’s measurement. Left column: recorded images. Right column: line profiles.

Equations (4)

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

Φ ( t = 0 ) = Ψ 1 1 2 ( 0 2 0 3 + 1 2 1 3 ) .
Φ ( t = 0 ) = 1 2 ( α 0 1 0 2 + β 1 1 0 2 ) 0 3 + 1 2 ( α 0 1 1 2 + β 1 1 1 2 ) 1 3 .
Φ ( t = 1 ) = 1 2 0 1 0 2 ( α 0 + β 1 ) 3 + 1 2 0 1 1 2 ( α 1 + β 0 ) 3 + 1 2 1 1 0 2 ( α 0 β 1 ) 3 + 1 2 1 1 1 2 ( α 1 β 0 ) 3 .
U = e i α [ 1 0 0 e i β ] [ cos γ 2 sin γ 2 sin γ 2 cos γ 2 ] [ 1 0 0 e i δ ] ,

Metrics