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arXiv:quant-ph/0411108

Framework for quantum modeling of fiber-optical networks: PART II

John M. Myers

Published Nov 15, 2004• 2 citations
arXivHTMLPDF

Abstract

We formulate quantum optics to include frequency dependence in the modeling of optical networks. Entangled light pulses available for quantum cryptography are entangled not only in polarization but also, whether one wants it or not, in frequency. We model effects of the frequency spectrum of faint polarization-entangled light pulses on detection statistics. For instance, we show how polarization entanglement combines with frequency entanglement in the variation of detection statistics with pulse energy. Attention is paid not only to single-photon light states but also to multi-photon states. These are needed (1) to analyze the dependence of statistics on energy and (2) to help in calibrating fiber couplers, lasers and other devices, even when their desired use is for the generation of single-photon light.

DOI
10.48550/arxiv.quant-ph/0411108

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We formulate quantum optics to include frequency dependence in the modeling of optical networks. Entangled light pulses available for quantum cryptography are entangled not only in polarization but also, whether one wants it or not, in frequency. We model effects of the frequency spectrum of faint polarization-entangled light pulses on detection statistics. For instance, we show how polarization entanglement combines with frequency entanglement in the variation of detection statistics with pulse energy. Attention is paid not only to single-photon light states but also to multi-photon states. These are needed (1) to analyze the dependence of statistics on energy and (2) to help in calibrating fiber couplers, lasers and other devices, even when their desired use is for the generation of single-photon light.
We formulate quantum optics to include frequency dependence in the modeling of optical networks. Entangled light pulses available for quantum cryptography are entangled not only in polarization but also, whether one wants it or not, in frequency. We model effects of the frequency spectrum of faint polarization-entangled light pulses on detection statistics. For instance, we show how polarization entanglement combines with frequency entanglement in the variation of detection statistics with pulse energy. Attention is paid not only to single-photon light states but also to multi-photon states. These are needed (1) to analyze the dependence of statistics on energy and (2) to help in calibrating fiber couplers, lasers and other devices, even when their desired use is for the generation of single-photon light.
With the recognition of a logical gap between experiments and equations of quantum mechanics comes: (1) a chance to clarify such purely mathematical entities as probabilities, density operators, and partial traces-separated out from the choices and judgments necessary to apply them to describing experiments with devices, and (2) an added freedom to invent equations by which to model devices, stemming from the corresponding freedom in interpreting how these equations connect to experiments. Here I apply a few of these clarifications and freedoms to model polarization-entangled light pulses called for in quantum key distribution (QKD). Available light pulses are entangled not only in polarization but also in frequency. Although absent from the simplified models that initiated QKD, the degree of frequency entanglement of polarization-entangled light pulses is shown to affect the amount of key that can be distilled from raw light signals, in one case by a factor of 4/3. Open questions remain, because QKD brings concepts of quantum decision theory, such as measures of distinguishability, mostly worked out in the context of finite-dimensional vector spaces, into contact with infinite-dimensional Hilbert spaces needed to give expression to optical frequency spectra.
At the heart of quantum physics lies the principle of superposition, and at the heart of information theory lies the bit. Perhaps the most useful property of quantum systems is that they can be loaded with information bits, so-called qubits, that are indefinitely both 0 and 1 until a measurement is made. Another consequence is that several qubits can become entangled, which is manifested by the non-classical correlations between such quantum systems when measured in all possible bases. Within the rapidly progressing fields of quantum information and quantum communication these quantum effects are utilized to perform tasks such as quantum computing and quantum cryptography. In this thesis we present experimental and theoretical work using single photon sources to prepare ``flying'' photonic qubits. We describe work using mainly quasi-phase-matched nonlinear crystals to generate beams of entangled photon pairs, that are either encoded in polarization at near-visible wavelengths, or in time at optical fiber telecommunication wavelengths (1550 nm). The optical fiber is the medium used for transporting the qubits over a long distance, and it is therefore essential to couple the photons well into the fibers. By focusing the beams optimally, we have investigated how this problem can meet the requirement of creating photons of a narrow frequency bandwidth and a high photon flux. Furthermore, we have generated truly single photons that are heralded by an electrical signal. As a result of modifying the statistics of such sources we have been able to show the effect of photon antibunching. In two separate works, we have implemented a quantum key distribution system based on faint laser pulses at the telecom wavelength of 1550 nm, as well as protocols based on entanglement for performing authentication of key distribution in quantum cryptography.
Quantum laws can be used to implement secure communication channels; this has been named quantum cryptography. In quantum cryptography the security does not depend of limited computational power, but is inherent to the laws that govern the propagation and detection of single and entangled photons. We show how single and entangled photon-pairs can be efficiently generated using four-wave mixing in optical fibers. We analyze the source statistics, degree of entanglement and impact of spontaneous Raman scattering. By coding information in the photons polarization we are able to transmit quantum information over 20 km of standard single mode fiber.
Quantum optics has attracted significant interest owing to its potential for novel applications in fields such as computing, communication, and sensing. With advancements in single photon generation and detection in the telecom band, quantum remote applications utilizing the nonlocality of entangled photon pairs are becoming increasingly viable. In this study, we demonstrate quantum remote spectroscopy by transmitting frequency entangled photons through a real-world fiber network. In the experiment, entangled photon pairs in the telecom band (photon 1 and photon 2) were generated via spontaneous parametric down-conversion in a type-II PPMgSLT crystal using a mode-locked Ti:Sapphire laser (76MHz repetition rate, 792nm center wavelength). The photon pairs were separated with a fiber polarization beam splitter. Photon 1 was transmitted through a 2.6-km real-world fiber network and programmable spectral filter, serving as the sample under investigation. Both photons were detected using superconducting single photon detectors (SSPDs). Quantum frequency correlation, termed joint spectral intensity (JSI), was obtained as a two-dimensional histogram utilizing coincidence counting and time-stretch methods. The spectrum of photon 2, which did not transmit fiber network and spectral filter, was obtained by projecting the JSI. Although photon 1 interact with the fiber network and programmable filter, the spectrum of photon 2 exhibited strong agreement with the reference spectrum defined by programmable filter. Finally, one photon of the pair was transmitted over a 2.6km real-world fiber network with a fiber sensor. Using quantum frequency correlation, the spectral information of the fiber sensor was deduced remotely from the spectrum of the counter part of the photon, which did not directly interact with the sensor. This demonstrated the feasibility of remote spectroscopic sensing using frequency entanglement via a real-world fiber network. The findings pave the way for practical quantum remote spectroscopy, obviating the need for sophisticated spectroscopic equipment at the remote site.