Alex Dixon - Academia.edu (original) (raw)

Papers by Alex Dixon

Research paper thumbnail of Practical gigahertz quantum key distribution based on avalanche photodiodes

New Journal of Physics, 2009

We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only prac... more We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only practical components. Compact semiconductor avalanche photodiodes are used for high-speed single photon detection, whereas an attenuated laser is used as a light source in combination with the decoy protocol for guarding against photon-number-splitting attacks. The system is characterized by secure key rates of 1.02 Mbit s-1 for a fibre distance of 20 km and 10.1 kbit s-1 for 100 km. The suitability of standard single mode fibres as the quantum channel is also demonstrated.

Research paper thumbnail of Megabit per second quantum key distribution using practical InGaAs APDs

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with ... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with a record secure key rate of 1.02 Mbit/s over a fiber distance of 20 km and 10.1 kbit/s over 100 km.

Research paper thumbnail of Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate

Optics Express, 2008

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key r... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key rates have been achieved thanks to the use of self-differencing InGaAs avalanche photodiodes designed specifically for high speed single photon detection. The system is characterized with a secure key rate of 1.02 Mbit/s for a fiber distance of 20 km and 10.1 kbit/s for 100 km. As the present advance relies upon compact non-cryogenic detectors, it opens the door towards practical and low cost QKD systems to secure broadband communication in future.

Research paper thumbnail of Gigahertz quantum key distribution with InGaAs avalanche photodiodes

Applied Physics Letters, 2008

We report a demonstration of quantum key distribution (QKD) at gigahertz clock rates with InGaAs ... more We report a demonstration of quantum key distribution (QKD) at gigahertz clock rates with InGaAs avalanche photodiodes (APDs) operating in a self-differencing mode. Such a mode of operation allows detection of extremely weak avalanches so that the detector afterpulse noise is sufficiently suppressed. The system is characterized by a secure bit rate of 2.37 Mbit/s at 5.6 km and 27.9 kbit/s at 65.5 km when the fiber dispersion is not compensated. After compensating the fiber dispersion, the QKD distance is extended to 101 km, resulting in a secure key rate of 2.88 kbit/s. Our results suggest that InGaAs APDs are very well suited to gigahertz QKD applications.

Research paper thumbnail of Gigahertz quantum key distribution with 1 Mbit/s secure key rate using decoy pulses

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with ... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with a record secure key rate of 1.02 Mbit/s over a fibre distance of 20 km and 10.1 kbit/s over 100 km.

Research paper thumbnail of Multi-gigahertz photon counting using InGaAs APDs

We demonstrate multi-gigahertz photon-counting at 1550nm using self-differencing In-GaAs APDs. Th... more We demonstrate multi-gigahertz photon-counting at 1550nm using self-differencing In-GaAs APDs. The quantum efficiency is characterized as 23.5% at an after-pulse probability of 4.84%. The device will further increase the bit-rate for fiber quantum key distribution.

Research paper thumbnail of Multi-gigahertz operation of photon counting InGaAs avalanche photodiodes

Applied Physics Letters, 2010

We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection... more We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection at telecom wavelengths. Employing a self-differencing circuit that incorporates tuneability in both frequency and arm balancing, extremely weak avalanches can now be sensed so as to suppress afterpulsing. The afterpulse probability is characterized as 4.84% and 1.42% for a photon detection efficiency of 23.5% and 11.8%, respectively. The device will further increase the secure bit rate for fiber wavelength quantum key distribution.

Research paper thumbnail of Single photon detection for high bit rate quantum communication

Quantum communication, in particular, quantum key distribution (QKD) is moving ever closer to rea... more Quantum communication, in particular, quantum key distribution (QKD) is moving ever closer to real world implementation. However, for successful QKD system deployment, the QKD system components must be robustly designed and feature highly reliable operation. In this paper we focus on one important aspect of any quantum communication system: the single photon detector. In particular our interest is centered upon the InGaAs avalanche photodiode (APD) single photon detector operating in a self-differencing (SD) mode. Such a detector features high clock frequencies of up to 3GHz, high photon count rates as well as detection efficiencies approaching 20% with low afterpulsing. We show successful operation of a high bit rate QKD system using this SD-APD technology in a real world fiber network.

Research paper thumbnail of Ultrashort dead time of photon-counting InGaAs avalanche photodiodes

Applied Physics Letters, 2009

We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of... more We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of just 1.93 ns. This is demonstrated by full recovery of the detection efficiency two gate cycles after a detection event, as well as a measured maximum detection rate of 497 MHz. As an application, we measure the second order correlation function g(2) of the emission from a diode laser with a single detector that works reliably at high speed owing to the extremely short dead time of the detector. The device is ideal for high bit rate fiber wavelength quantum key distribution and photonic quantum computing.

Research paper thumbnail of Ultrashort dead time of photon-counting InGaAs avalanche photodiodes

We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of... more We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of just 1.93 ns. This is demonstrated by full recovery of the detection efficiency two gate cycles after a detection event, as well as a measured maximum detection rate of 497 MHz. As an application, we measure the second order correlation function g (2) of the emission from a diode laser with a single detector which works reliably at high speed owing to the extremely short dead time of the detector. The device is ideal for high bit rate fiber wavelength quantum key distribution and photonic quantum computing.

Research paper thumbnail of Actively stabilised quantum key distribution operating continuously at 1 Mbit/s

We report the continuous operation of an actively stabilised gigahertz clocked quantum key distri... more We report the continuous operation of an actively stabilised gigahertz clocked quantum key distribution (QKD) system, with an average secure key rate of 1 Mbit/s over a distance of 50 km.

Research paper thumbnail of Practical gigahertz quantum key distribution based on avalanche photodiodes

New Journal of Physics, 2009

We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only prac... more We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only practical components. Compact semiconductor avalanche photodiodes are used for high-speed single photon detection, whereas an attenuated laser is used as a light source in combination with the decoy protocol for guarding against photon-number-splitting attacks. The system is characterized by secure key rates of 1.02 Mbit s −1 for a fibre distance of 20 km and 10.1 kbit s −1 for 100 km. The suitability of standard single mode fibres as the quantum channel is also demonstrated. References 10

Research paper thumbnail of Continuous operation of high bit rate quantum key distribution

Applied Physics Letters, 2010

We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fi... more We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fiber averaged over a continuous 36 h period. Continuous operation of high bit rates is achieved using feedback systems to control path length difference and polarization in the interferometer and the timing of the detection windows. High bit rates and continuous operation allows finite key size effects to be strongly reduced, achieving a key extraction efficiency of 96% compared to keys of infinite lengths.

Research paper thumbnail of Multi-gigahertz operation of photon counting InGaAs avalanche photodiodes

We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection... more We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection at telecom wavelengths. Employing a self-differencing circuit that incorporates tuneability in both frequency and arm balancing, extremely weak avalanches can now be sensed so as to suppress afterpulsing. The afterpulse probability is characterized as 4.84% and 1.42% for a photon detection efficiency of 23.5% and 11.8%, respectively. The device will further increase the secure bit rate for fiber wavelength quantum key distribution.

Research paper thumbnail of Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate

Optics Express, 2008

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key r... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key rates have been achieved thanks to the use of self-differencing InGaAs avalanche photodiodes designed specifically for high speed single photon detection. The system is characterized with a secure key rate of 1.02 Mbit/s for a fiber distance of 20 km and 10.1 kbit/s for 100 km. As the present advance relies upon compact non-cryogenic detectors, it opens the door towards practical and low cost QKD systems to secure broadband communication in future.

Research paper thumbnail of Gigahertz quantum key distribution with InGaAs avalanche photodiodes

We report a demonstration of quantum key distribution (QKD) at GHz clock rates with InGaAs avalan... more We report a demonstration of quantum key distribution (QKD) at GHz clock rates with InGaAs avalanche photodiodes (APDs) operating in a self-differencing mode. Such a mode of operation allows detection of extremely weak avalanches so that the detector afterpulse noise is sufficiently suppressed. The system is characterized by a secure bit rate of 2.37 Mbps at 5.6 km and 27.9 kbps at 65.5 km when the fiber dispersion is not compensated. After compensating the fiber dispersion, the QKD distance is extended to 101 km, resulting in a secure key rate of 2.88 kbps. Our results suggest that InGaAs APDs are very well suited to GHz QKD applications.

Research paper thumbnail of Gigacounts/s photon detection and its applications

I. INTRODUCTION Single photon detectors at telecom wavelengths are prerequisite for implementing ... more I. INTRODUCTION Single photon detectors at telecom wavelengths are prerequisite for implementing long-distance quantum communication protocols, such as quantum key distribution (QKD) and entanglement distribution. The bit rates of these protocols are often severely limited by the detector performance. Until recently the secure bit rate for QKD has been limited to just a few kilobits/s [1]. While sufficient for point-to-point encrypted links with AES encryption, much higher bit rates will be required in realistic networks where the bit rate is shared between many users/ ...

Research paper thumbnail of Continuous operation of high bit rate quantum key distribution

We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fi... more We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fiber averaged over a continuous 36-hours period. Continuous operation of high bit rates is achieved using feedback systems to control path length difference and polarization in the interferometer and the timing of the detection windows. High bit rates and continuous operation allows finite key size effects to be strongly reduced, achieving a key extraction efficiency of 96% compared to keys of infinite lengths.

Research paper thumbnail of Anomalously Slow Attrition Times for Asymmetric Populations with Internal Group Dynamics

Physical Review Letters, 2009

The many-body dynamics exhibited by living objects include group formation within a population an... more The many-body dynamics exhibited by living objects include group formation within a population and the nonequilibrium process of attrition between two opposing populations due to competition or conflict. We show analytically and numerically that the combination of these two dynamical processes generates an attrition duration T whose nonlinear dependence on population asymmetry x is in stark contrast to standard mass-action theories. A minority population experiences a longer survival time than two equally balanced populations, irrespective of whether or not the majority population adopts such an internal grouping. Adding a third population with predefined group sizes allows T(x) to be tailored. Our findings compare favorably to real-world observations.

Research paper thumbnail of Statistical physics and modern human warfare

Modern human conflicts, such as those ongoing in Iraq, Afghanistan and Colombia, typically involv... more Modern human conflicts, such as those ongoing in Iraq, Afghanistan and Colombia, typically involve a large conventional force (e.g., a state army) fighting a relatively small insurgency having a loose internal structure. In this chapter, we adopt this qualitative picture in order to study the dynamics – and in particular the duration – of modern wars involving a loose insurgent force. We generalize a coalescence-fragmentation model from the statistical physics community in order to describe the insurgent population, and find that the resulting behavior is qualitatively different from conventional mass-action approaches. One of our main results is a counterintuitive relationship between an insurgent war’s duration and the asymmetry between the two opposing forces, a prediction which is borne out by empirical observation.

Research paper thumbnail of Practical gigahertz quantum key distribution based on avalanche photodiodes

New Journal of Physics, 2009

We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only prac... more We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only practical components. Compact semiconductor avalanche photodiodes are used for high-speed single photon detection, whereas an attenuated laser is used as a light source in combination with the decoy protocol for guarding against photon-number-splitting attacks. The system is characterized by secure key rates of 1.02 Mbit s-1 for a fibre distance of 20 km and 10.1 kbit s-1 for 100 km. The suitability of standard single mode fibres as the quantum channel is also demonstrated.

Research paper thumbnail of Megabit per second quantum key distribution using practical InGaAs APDs

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with ... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with a record secure key rate of 1.02 Mbit/s over a fiber distance of 20 km and 10.1 kbit/s over 100 km.

Research paper thumbnail of Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate

Optics Express, 2008

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key r... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key rates have been achieved thanks to the use of self-differencing InGaAs avalanche photodiodes designed specifically for high speed single photon detection. The system is characterized with a secure key rate of 1.02 Mbit/s for a fiber distance of 20 km and 10.1 kbit/s for 100 km. As the present advance relies upon compact non-cryogenic detectors, it opens the door towards practical and low cost QKD systems to secure broadband communication in future.

Research paper thumbnail of Gigahertz quantum key distribution with InGaAs avalanche photodiodes

Applied Physics Letters, 2008

We report a demonstration of quantum key distribution (QKD) at gigahertz clock rates with InGaAs ... more We report a demonstration of quantum key distribution (QKD) at gigahertz clock rates with InGaAs avalanche photodiodes (APDs) operating in a self-differencing mode. Such a mode of operation allows detection of extremely weak avalanches so that the detector afterpulse noise is sufficiently suppressed. The system is characterized by a secure bit rate of 2.37 Mbit/s at 5.6 km and 27.9 kbit/s at 65.5 km when the fiber dispersion is not compensated. After compensating the fiber dispersion, the QKD distance is extended to 101 km, resulting in a secure key rate of 2.88 kbit/s. Our results suggest that InGaAs APDs are very well suited to gigahertz QKD applications.

Research paper thumbnail of Gigahertz quantum key distribution with 1 Mbit/s secure key rate using decoy pulses

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with ... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD) system, with a record secure key rate of 1.02 Mbit/s over a fibre distance of 20 km and 10.1 kbit/s over 100 km.

Research paper thumbnail of Multi-gigahertz photon counting using InGaAs APDs

We demonstrate multi-gigahertz photon-counting at 1550nm using self-differencing In-GaAs APDs. Th... more We demonstrate multi-gigahertz photon-counting at 1550nm using self-differencing In-GaAs APDs. The quantum efficiency is characterized as 23.5% at an after-pulse probability of 4.84%. The device will further increase the bit-rate for fiber quantum key distribution.

Research paper thumbnail of Multi-gigahertz operation of photon counting InGaAs avalanche photodiodes

Applied Physics Letters, 2010

We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection... more We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection at telecom wavelengths. Employing a self-differencing circuit that incorporates tuneability in both frequency and arm balancing, extremely weak avalanches can now be sensed so as to suppress afterpulsing. The afterpulse probability is characterized as 4.84% and 1.42% for a photon detection efficiency of 23.5% and 11.8%, respectively. The device will further increase the secure bit rate for fiber wavelength quantum key distribution.

Research paper thumbnail of Single photon detection for high bit rate quantum communication

Quantum communication, in particular, quantum key distribution (QKD) is moving ever closer to rea... more Quantum communication, in particular, quantum key distribution (QKD) is moving ever closer to real world implementation. However, for successful QKD system deployment, the QKD system components must be robustly designed and feature highly reliable operation. In this paper we focus on one important aspect of any quantum communication system: the single photon detector. In particular our interest is centered upon the InGaAs avalanche photodiode (APD) single photon detector operating in a self-differencing (SD) mode. Such a detector features high clock frequencies of up to 3GHz, high photon count rates as well as detection efficiencies approaching 20% with low afterpulsing. We show successful operation of a high bit rate QKD system using this SD-APD technology in a real world fiber network.

Research paper thumbnail of Ultrashort dead time of photon-counting InGaAs avalanche photodiodes

Applied Physics Letters, 2009

We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of... more We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of just 1.93 ns. This is demonstrated by full recovery of the detection efficiency two gate cycles after a detection event, as well as a measured maximum detection rate of 497 MHz. As an application, we measure the second order correlation function g(2) of the emission from a diode laser with a single detector that works reliably at high speed owing to the extremely short dead time of the detector. The device is ideal for high bit rate fiber wavelength quantum key distribution and photonic quantum computing.

Research paper thumbnail of Ultrashort dead time of photon-counting InGaAs avalanche photodiodes

We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of... more We report a 1.036 GHz gated Geiger mode InGaAs avalanche photodiode with a detection dead time of just 1.93 ns. This is demonstrated by full recovery of the detection efficiency two gate cycles after a detection event, as well as a measured maximum detection rate of 497 MHz. As an application, we measure the second order correlation function g (2) of the emission from a diode laser with a single detector which works reliably at high speed owing to the extremely short dead time of the detector. The device is ideal for high bit rate fiber wavelength quantum key distribution and photonic quantum computing.

Research paper thumbnail of Actively stabilised quantum key distribution operating continuously at 1 Mbit/s

We report the continuous operation of an actively stabilised gigahertz clocked quantum key distri... more We report the continuous operation of an actively stabilised gigahertz clocked quantum key distribution (QKD) system, with an average secure key rate of 1 Mbit/s over a distance of 50 km.

Research paper thumbnail of Practical gigahertz quantum key distribution based on avalanche photodiodes

New Journal of Physics, 2009

We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only prac... more We report in this paper a gigahertz clocked quantum key distribution (QKD) system using only practical components. Compact semiconductor avalanche photodiodes are used for high-speed single photon detection, whereas an attenuated laser is used as a light source in combination with the decoy protocol for guarding against photon-number-splitting attacks. The system is characterized by secure key rates of 1.02 Mbit s −1 for a fibre distance of 20 km and 10.1 kbit s −1 for 100 km. The suitability of standard single mode fibres as the quantum channel is also demonstrated. References 10

Research paper thumbnail of Continuous operation of high bit rate quantum key distribution

Applied Physics Letters, 2010

We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fi... more We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fiber averaged over a continuous 36 h period. Continuous operation of high bit rates is achieved using feedback systems to control path length difference and polarization in the interferometer and the timing of the detection windows. High bit rates and continuous operation allows finite key size effects to be strongly reduced, achieving a key extraction efficiency of 96% compared to keys of infinite lengths.

Research paper thumbnail of Multi-gigahertz operation of photon counting InGaAs avalanche photodiodes

We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection... more We report a 2 GHz operation of InGaAs avalanche photodiodes for efficient single photon detection at telecom wavelengths. Employing a self-differencing circuit that incorporates tuneability in both frequency and arm balancing, extremely weak avalanches can now be sensed so as to suppress afterpulsing. The afterpulse probability is characterized as 4.84% and 1.42% for a photon detection efficiency of 23.5% and 11.8%, respectively. The device will further increase the secure bit rate for fiber wavelength quantum key distribution.

Research paper thumbnail of Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate

Optics Express, 2008

We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key r... more We report the first gigahertz clocked decoy-protocol quantum key distribution (QKD). Record key rates have been achieved thanks to the use of self-differencing InGaAs avalanche photodiodes designed specifically for high speed single photon detection. The system is characterized with a secure key rate of 1.02 Mbit/s for a fiber distance of 20 km and 10.1 kbit/s for 100 km. As the present advance relies upon compact non-cryogenic detectors, it opens the door towards practical and low cost QKD systems to secure broadband communication in future.

Research paper thumbnail of Gigahertz quantum key distribution with InGaAs avalanche photodiodes

We report a demonstration of quantum key distribution (QKD) at GHz clock rates with InGaAs avalan... more We report a demonstration of quantum key distribution (QKD) at GHz clock rates with InGaAs avalanche photodiodes (APDs) operating in a self-differencing mode. Such a mode of operation allows detection of extremely weak avalanches so that the detector afterpulse noise is sufficiently suppressed. The system is characterized by a secure bit rate of 2.37 Mbps at 5.6 km and 27.9 kbps at 65.5 km when the fiber dispersion is not compensated. After compensating the fiber dispersion, the QKD distance is extended to 101 km, resulting in a secure key rate of 2.88 kbps. Our results suggest that InGaAs APDs are very well suited to GHz QKD applications.

Research paper thumbnail of Gigacounts/s photon detection and its applications

I. INTRODUCTION Single photon detectors at telecom wavelengths are prerequisite for implementing ... more I. INTRODUCTION Single photon detectors at telecom wavelengths are prerequisite for implementing long-distance quantum communication protocols, such as quantum key distribution (QKD) and entanglement distribution. The bit rates of these protocols are often severely limited by the detector performance. Until recently the secure bit rate for QKD has been limited to just a few kilobits/s [1]. While sufficient for point-to-point encrypted links with AES encryption, much higher bit rates will be required in realistic networks where the bit rate is shared between many users/ ...

Research paper thumbnail of Continuous operation of high bit rate quantum key distribution

We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fi... more We demonstrate a quantum key distribution with a secure bit rate exceeding 1 Mbit/s over 50 km fiber averaged over a continuous 36-hours period. Continuous operation of high bit rates is achieved using feedback systems to control path length difference and polarization in the interferometer and the timing of the detection windows. High bit rates and continuous operation allows finite key size effects to be strongly reduced, achieving a key extraction efficiency of 96% compared to keys of infinite lengths.

Research paper thumbnail of Anomalously Slow Attrition Times for Asymmetric Populations with Internal Group Dynamics

Physical Review Letters, 2009

The many-body dynamics exhibited by living objects include group formation within a population an... more The many-body dynamics exhibited by living objects include group formation within a population and the nonequilibrium process of attrition between two opposing populations due to competition or conflict. We show analytically and numerically that the combination of these two dynamical processes generates an attrition duration T whose nonlinear dependence on population asymmetry x is in stark contrast to standard mass-action theories. A minority population experiences a longer survival time than two equally balanced populations, irrespective of whether or not the majority population adopts such an internal grouping. Adding a third population with predefined group sizes allows T(x) to be tailored. Our findings compare favorably to real-world observations.

Research paper thumbnail of Statistical physics and modern human warfare

Modern human conflicts, such as those ongoing in Iraq, Afghanistan and Colombia, typically involv... more Modern human conflicts, such as those ongoing in Iraq, Afghanistan and Colombia, typically involve a large conventional force (e.g., a state army) fighting a relatively small insurgency having a loose internal structure. In this chapter, we adopt this qualitative picture in order to study the dynamics – and in particular the duration – of modern wars involving a loose insurgent force. We generalize a coalescence-fragmentation model from the statistical physics community in order to describe the insurgent population, and find that the resulting behavior is qualitatively different from conventional mass-action approaches. One of our main results is a counterintuitive relationship between an insurgent war’s duration and the asymmetry between the two opposing forces, a prediction which is borne out by empirical observation.