T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, “Performing high-quality multi-photon experiments with parametric down-conversion,” J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).

[Crossref]

S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion,” Phys. Rev. A 77, 043807 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Nonlocal dispersion control of a single-photon waveform,” Phys. Rev. A 78, 013816 (2008).

[Crossref]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography,” Phys. Rev. Lett. 91, 083601 (2003).

[Crossref]
[PubMed]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).

[Crossref]
[PubMed]

M. J. Fitch and J. D. Franson, “Dispersion cancellation and nonclassical noise reduction for large-photon-number states,” Phys. Rev. A 65, 053809 (2002).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature (London) 412, 417–419 (2001).

[Crossref]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, “Quantum teleportation of a polarization state with a complete bell state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).

[Crossref]
[PubMed]

J. Brendel, H. Zbinden, and N. Gisin, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. 151, 35–39 (1998).

[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349–5360 (1996).

[Crossref]
[PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).

[Crossref]
[PubMed]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).

[Crossref]
[PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).

[Crossref]
[PubMed]

E. B. Treacy, “Optical Pulse CompressionWith Diffraction Gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).

[Crossref]

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, “Performing high-quality multi-photon experiments with parametric down-conversion,” J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).

[Crossref]

S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion,” Phys. Rev. A 77, 043807 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Nonlocal dispersion control of a single-photon waveform,” Phys. Rev. A 78, 013816 (2008).

[Crossref]

J. Brendel, H. Zbinden, and N. Gisin, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. 151, 35–39 (1998).

[Crossref]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).

[Crossref]
[PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).

[Crossref]
[PubMed]

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, Burlington, MA, 2006).

M. J. Fitch and J. D. Franson, “Dispersion cancellation and nonclassical noise reduction for large-photon-number states,” Phys. Rev. A 65, 053809 (2002).

[Crossref]

M. J. Fitch and J. D. Franson, “Dispersion cancellation and nonclassical noise reduction for large-photon-number states,” Phys. Rev. A 65, 053809 (2002).

[Crossref]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).

[Crossref]
[PubMed]

J. D. Franson, Proceedings of the 9th Rochester Conference on Coherence and Quantum Optics, eds. N. P. Bigelow, J. H. Eberly, and C. R. Stroud, “Nonlocal Interferometry: Beyond Bell’s Inequality,” Jr. (American Institute of Physics, 2008).

J. D. Franson, “Nonclassical Nature of Dispersion Cancellation and Nonlocal Interferometry,” prreprintarXiv: 0907.5196 (2009).

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature (London) 412, 417–419 (2001).

[Crossref]

J. Brendel, H. Zbinden, and N. Gisin, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. 151, 35–39 (1998).

[Crossref]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).

[Crossref]
[PubMed]

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, “Performing high-quality multi-photon experiments with parametric down-conversion,” J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).

[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Nonlocal dispersion control of a single-photon waveform,” Phys. Rev. A 78, 013816 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).

[Crossref]

S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion,” Phys. Rev. A 77, 043807 (2008).

[Crossref]

Y.-H. Kim and W. P. Grice, “Measurement of the spectral properties of the two-photon state generated via type II spontaneous parametric downconversion,” Opt. Lett. 30, 908–910 (2005).

[Crossref]
[PubMed]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, “Quantum teleportation of a polarization state with a complete bell state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).

[Crossref]
[PubMed]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, “Quantum teleportation of a polarization state with a complete bell state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).

[Crossref]
[PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).

[Crossref]
[PubMed]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Nonlocal dispersion control of a single-photon waveform,” Phys. Rev. A 78, 013816 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature (London) 412, 417–419 (2001).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature (London) 412, 417–419 (2001).

[Crossref]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).

[Crossref]
[PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography,” Phys. Rev. Lett. 91, 083601 (2003).

[Crossref]
[PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).

[Crossref]
[PubMed]

P. P. Rohde and T. C. Ralph, “Optimal photons for quantum information processing,” Phys. Rev. A 72, 052332 (2005).

[Crossref]

P. P. Rohde and T. C. Ralph, “Optimal photons for quantum information processing,” Phys. Rev. A 72, 052332 (2005).

[Crossref]

M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349–5360 (1996).

[Crossref]
[PubMed]

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, Burlington, MA, 2006).

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography,” Phys. Rev. Lett. 91, 083601 (2003).

[Crossref]
[PubMed]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley & Sons, Hoboken, New Jersey, 2007).

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography,” Phys. Rev. Lett. 91, 083601 (2003).

[Crossref]
[PubMed]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).

[Crossref]
[PubMed]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, “Quantum teleportation of a polarization state with a complete bell state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).

[Crossref]
[PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).

[Crossref]
[PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography,” Phys. Rev. Lett. 91, 083601 (2003).

[Crossref]
[PubMed]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley & Sons, Hoboken, New Jersey, 2007).

E. B. Treacy, “Optical Pulse CompressionWith Diffraction Gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).

[Crossref]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).

[Crossref]
[PubMed]

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, “Performing high-quality multi-photon experiments with parametric down-conversion,” J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).

[Crossref]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).

[Crossref]
[PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

J. Brendel, H. Zbinden, and N. Gisin, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. 151, 35–39 (1998).

[Crossref]

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, “Performing high-quality multi-photon experiments with parametric down-conversion,” J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).

[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

E. B. Treacy, “Optical Pulse CompressionWith Diffraction Gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).

[Crossref]

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, “Performing high-quality multi-photon experiments with parametric down-conversion,” J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).

[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature (London) 412, 417–419 (2001).

[Crossref]

J. Brendel, H. Zbinden, and N. Gisin, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. 151, 35–39 (1998).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).

[Crossref]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Nonlocal dispersion control of a single-photon waveform,” Phys. Rev. A 78, 013816 (2008).

[Crossref]

S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion,” Phys. Rev. A 77, 043807 (2008).

[Crossref]

M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349–5360 (1996).

[Crossref]
[PubMed]

P. P. Rohde and T. C. Ralph, “Optimal photons for quantum information processing,” Phys. Rev. A 72, 052332 (2005).

[Crossref]

M. J. Fitch and J. D. Franson, “Dispersion cancellation and nonclassical noise reduction for large-photon-number states,” Phys. Rev. A 65, 053809 (2002).

[Crossref]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).

[Crossref]
[PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).

[Crossref]
[PubMed]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, “Quantum teleportation of a polarization state with a complete bell state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).

[Crossref]
[PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).

[Crossref]
[PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography,” Phys. Rev. Lett. 91, 083601 (2003).

[Crossref]
[PubMed]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).

[Crossref]
[PubMed]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violations of Bell’s Inequality under Strict Einstein Locality Conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).

[Crossref]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley & Sons, Hoboken, New Jersey, 2007).

The gratings G1 and G2 are Spectrogon model 715.701.990 and 715.701.350, respectively. Both gratings have the same line spacing (2400 grooves/mm) and blaze wavelength (800 nm) but different in size. The detailed specifications can be found at http://www.spectrogon.com/gratpulse.html.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, Burlington, MA, 2006).

The measurement errors are mainly from measuring the distance G, ±1 mm, and the angle θ′, ±2°.

The demonstration in Ref. [8] is local in the sense that both photons propagate through the same optical fiber. Furthermore, actual reduction of a broadened wave packet is not experimentally demonstrated.

We have assumed γ 2D4L4≪(β1z1+β2z2)2. This condition holds in general as the crystal parameter DL is much smaller than the external parameters β1z1 and β2z2.

Dispersion cancellation of Ref. [10, 11] is based on Hong-Ou-Mandel interference in which two photons meet again before getting detected. It, therefore, is not a nonlocal effect and there exists a classical analog. On the other hand, in the nonlocal dispersion cancellation of Ref. [1], dispersion experienced by one photon is nonlocally cancelled by dispersion experienced by it’s entangled pair photon which may be arbitrarily far apart. See Ref. [13, 14].

J. D. Franson, Proceedings of the 9th Rochester Conference on Coherence and Quantum Optics, eds. N. P. Bigelow, J. H. Eberly, and C. R. Stroud, “Nonlocal Interferometry: Beyond Bell’s Inequality,” Jr. (American Institute of Physics, 2008).

J. D. Franson, “Nonclassical Nature of Dispersion Cancellation and Nonlocal Interferometry,” prreprintarXiv: 0907.5196 (2009).