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arXiv:quant-ph/0201075 · Physical Review A

Dispersion cancellation and nonclassical noise reduction for large-photon-number states

Michael J. Fitch, J. D. Franson

Published Apr 24, 2002• 17 citations
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Abstract

Nonlocal dispersion cancellation is generalized to frequency-entangled states with large photon number N. We show that the same entangled states can simultaneously exhibit a factor of $1/\sqrt{N}$ reduction in noise below the classical shot noise limit in precise timing applications, as was previously suggested by Giovannetti, Lloyd, and Maccone [Nature (London) 412, 417 (2001)]. The quantum-mechanical noise reduction can be destroyed by a relatively small amount of uncompensated dispersion and entangled states of this kind have larger timing uncertainties than the corresponding classical states in that case. Similar results were obtained for correlated states, anticorrelated states, and frequency-entangled coherent states, which shows that these effects are a fundamental result of entanglement.

DOI
10.1103/physreva.65.053809

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Nonlocal dispersion cancellation is generalized to frequency-entangled states with large photon number N. We show that the same entangled states can simultaneously exhibit a factor of 1/N1/\sqrt{N}1/N​ reduction in noise below the classical shot noise limit in precise timing applications, as was previously suggested by Giovannetti, Lloyd, and Maccone [Nature (London) 412, 417 (2001)]. The quantum-mechanical noise reduction can be destroyed by a relatively small amount of uncompensated dispersion and entangled states of this kind have larger timing uncertainties than the corresponding classical states in that case. Similar results were obtained for correlated states, anticorrelated states, and frequency-entangled coherent states, which shows that these effects are a fundamental result of entanglement.
Summary form only given. Two classical pulses of light propagating through two distant, dispersive media will experience dispersion that depends only on the local properties of the two media. It was previously shown, however, that two entangled photons propagating through two dispersive media, can experience a cancellation of dispersion in the sense that the two photons will arrive at two equally-distant detectors at the same time despite the dispersion. Other forms of dispersion cancellation have also been described. We generalize dispersion cancellation to entangled states containing a large number N of photons in each pulse.
Shapiro recently argued that nonlocal dispersion cancellation using entangled pairs of photons is essentially classical in nature, based on a comparison with a classical model in which two stationary, chaotic beams of light have phases and frequencies that are anticorrelated, which he refers to as ``phase-sensitive'' light [J. H. Shapiro, Phys. Rev. A 81, 023824 (2010)]. It is shown here that there is no physical cancellation of dispersion for classical light of that kind and Shapiro's results merely reflect the fact that identical dispersion occurs in both beams. The origin of the cross correlations between the intensities of the two beams is shown to be completely different in the classical and quantum mechanical cases.
Benefiting from the unique quantum feature of nonlocal dispersion cancellation (NDC), the strong temporal correlation of frequency-entangled photon pair source can be maintained from the unavoidable dispersive propagation. It has thus played a major role in many fiber-based quantum information applications. However, the limit of NDC due to finite frequency entanglement has not been quantified. In this study, we provide a full theoretical analysis of the NDC characteristics for the photon pairs with finite frequency entanglement. Experimental examinations were conducted by using two spontaneous parametric down-conversion photon pair sources with frequency correlation and anticorrelation properties. The excellent agreement demonstrates the fundamental limit on the minimum temporal correlation width by the nonzero two-photon spectral correlation width of the paired photons, which introduces an inevitable broadening by interaction with the dispersion in the signal path. This study provides an easily accessible tool for assessing and optimizing the NDC in various quantum information applications.
The entanglement of quantum systems can produce a variety of nonclassical effects that have practical applications in quantum information science. One example of this is nonlocal dispersion cancellation, in which the effects of dispersion on one photon can be canceled out by the dispersion experienced by a second photon at a distant location. In this paper, we extend the analysis of nonlocal dispersion cancellation to three or more photons. We find that energy-time entanglement of three or more photons can lead to a complete or partial cancellation of dispersion depending on the experimental conditions. These results may be useful in implementing quantum key distribution in networks with three or more nodes.
Uncertainty relations are fundamental to quantum mechanics, encoding limits on the simultaneous measurement of conjugate observables. Violations of joint uncertainty bounds can certify entanglement -- a resource critical for quantum information protocols and increasingly relevant in strong-field physics. Here, we investigate the pairwise time-delay and frequency-bandwidth uncertainties for arbitrary multimode quantum states of light, deriving a general lower bound for their joint product. We find that the nonclassical correction scales inversely with the average photon number, a behavior rooted in the so-called ``monogamy of entanglement''. These results clarify the intensity scaling of quantum advantages in nonclassical light states and highlight the interplay between entanglement and photon statistics.
The observation of the so-called dispersion cancelation (Opt. Express 17, 19244, 2009) and temporal phase modulation (Phys. Rev. Lett. 103, 163601, 2009) of paired photons is generally attributed to the presence of frequency entanglement between two frequency anticorrelated photons. In this paper, it is shown that by introducing the appropriate amount of chromatic dispersion or phase modulation between non-entangled photons, it is also possible to observe these effects. Indeed, it is found that the relevant characteristic for the observation of dispersion cancelation or the cancelation of temporal phase modulation is the presence of certain frequency correlations between the photons.