Andrew S. Fletcher

Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel

Error correction procedures are considered which are designed specifically for the amplitude damping channel. Amplitude damping errors are analyzed in the stabilizer formalism. This analysis allows a generalization of the [4,1] ldquoapproximaterdquo amplitude damping code. This generalization is presented as a class of [2(M+1),M] codes; quantum circuits for encoding and recovery operations are presented. A [7,3] amplitude damping code based on the classical Hamming code is presented. All of these are stabilizer codes whose encoding and recovery operations can be completely described with Clifford group operations. Finally, optimization options are described in which recovery operations may be further adapted according to the damping probability gamma.

Overview of the Laser Communications Relay Demonstration Project

Abstract : This paper provides an overview of the Laser Communications Relay Demonstration Project (LCRD), a joint project between NASA?s Goddard Space Flight Center (GSFC), the Jet Propulsion Laboratory, California Institute of Technology (JPL), and the Massachusetts Institute of Technology Lincoln Laboratory (MIT/LL). LCRD will provide two years of continuous high data rate optical communications in an operational environment demonstrating how optical communications can meet NASA?s growing need for higher data rates, or for the same data rate provided by a comparable RF system, how it enables lower power, lower mass communications systems on user spacecraft. In addition, LCRD?s architecture will allow it to serve as a testbed in space for the development of additional symbol coding, link and network layer protocols, etc. This paper reviews the current concepts and designs for the flight and ground optical communications terminals, the critical technologies required, and the concept of operations. It reports preliminary conclusions from several trade studies conducted at GSFC, JPL, and MIT/LL. The flight optical communications terminals will be flown on a commercial communications satellite in geosynchronous orbit to be launched no earlier than December 2016, and will demonstrate a technology critical for NASA?s Next Generation Tracking and Data Relay Satellite.

Ultra-wide-range multi-rate DPSK laser communications

We propose and demonstrate a scalable high-sensitivity approach for achieving multi-rate DPSK using a single transmitter and fixed-interferometer-receiver design. Near-theoretical real-time performance is demonstrated over static and fading channels at rates from 2.4Mbps to 2.5Gbps.

Optimum quantum error recovery using semidefinite programming

Quantum error correction QEC is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded in a coded subspace, and error recovery is performed via an operation designed to perfectly correct for a set of errors, presumably a large subset of the physical noise process. In this paper, we examine the choice of recovery operation. Rather than seeking perfect correction on a subset of errors, we seek a recovery operation to maximize the entanglement fidelity for a given input state and noise model. In this way, the recovery operation is optimal for the given encoding and noise process. This optimization is shown to be calculable via a semidefinite program, a well-established form of convex optimization with efficient algorithms for its solution. The error recovery operation may also be interpreted as a combining operation following a quantum spreading channel, thus providing a quantum analogy to the classical diversity combining operation.

Structured near-optimal channel-adapted quantum error correction

We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace preserving (CPTP) constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality.

Undersea laser communication with narrow beams

Laser sources enable highly efficient optical communications links due to their ability to be focused into very directive beam profiles. Recent atmospheric and space optical links have demonstrated robust laser communications links at high rate with techniques that are applicable to the undersea environment. These techniques contrast to the broad-angle beams utilized in most reported demonstrations of undersea optical communications, which have employed LED-based transmitters. While the scattering in natural waters will cause the beam to broaden, a narrowly directive transmitter can still significantly increase the optical power delivered to a remote undersea terminal. Using Monte Carlo analysis of the undersea scattering environment, we show the two main advantages of narrow-beam optical communication: increased power throughput and decreased temporal spread. Based on information theoretic arguments, gigabit-per-second class links can be achieved at 20 extinction lengths by utilizing pulse position modulation, single-photon-sensitive receivers, and modern forward error correction techniques.

A multi-rate DPSK modem for free-space laser communications

The multi-rate DPSK format, which enables efficient free-space laser communications over a wide range of data rates, is finding applications in NASA’s Laser Communications Relay Demonstration. We discuss the design and testing of an efficient and robust multi-rate DPSK modem, including aspects of the electrical, mechanical, thermal, and optical design. The modem includes an optically preamplified receiver, an 0.5-W average power transmitter, a LEON3 rad-hard microcontroller that provides the command and telemetry interface and supervisory control, and a Xilinx Virtex-5 radhard reprogrammable FPGA that both supports the high-speed data flow to and from the modem and controls the modem’s analog and digital subsystems. For additional flexibility, the transmitter and receiver can be configured to support operation with multi-rate PPM waveforms.

Using DVB-S2 over asymmetric heterogeneous optical to radio frequency satellite links

The DVB-S2 coding standard has seen widespread use in many radio frequency (RF) communications applications. The availability of commercial-off-the-shelf (COTS) intellectual property (IP) that can be used to rapidly prototype and field communications systems makes this well-performing, standards-based approach to forward error correction (FEC) coding extremely attractive. In this paper, we evaluate the application of the DVB-S2 coding standard to an asymmetric satellite communications channel. The uplink comprises a fading optical link employing binary differential phase-shift keyed (DPSK) modulation, while the downlink comprises an RF link employing 16-ary amplitude and phase shift keyed (16-APSK) modulation. To simplify the payload implementation, hard-decision uplink demodulation is considered with uplink channel state information transmitted on the downlink for soft-decision decoding in the ground-based receiver. Additionally, we outline many of the tradeoffs in the overall system design, and some performance results of a baseline design are presented.

Long-haul atmospheric laser communication systems

Optical communications provides an attractive means of achieving wideband data transfer over long distances. We review perceived challenges and enabling technology developments that promise to facilitate a new era of free-space laser communications.

A narrow-beam undersea laser communications field demonstration

We report a demonstration of narrow-beam laser communication through the waters of Narragansett Bay in Rhode Island, USA. The transmitter and receiver were mounted on an aluminum truss and placed in the water alongside a pier operated by the Naval Undersea Warfare Center. The transmitter consisted of a real-time modulator and encoder, a 515 nm wavelength commercial laser, collimating optics, and a steering mirror. The receiver included a steering mirror, a focal plane camera, a linear-mode avalanche photo-diode (APD), a photo-multiplier tube (PMT) single photon detector, a large area imaging camera, an iris to vary the field of view, optics to split the beam between the various detectors, and field-programmable gate array (FPGA) electronics for real-time demodulation and decoding. The PMT and APD detectors were used for communications demonstrations; the imaging and focal plane cameras were used for channel characterization measurements and system alignment. Communications and characterization data were collected through a variety of conditions over the five day field experiment, including day and night, calm and high winds, and flood and ebb tide. In the experiment, the transmit power, receiver field of view, and link distance were varied. The water transmissivity and volume scattering function were measured throughout the experiment to calibrate the results. Real-time communications demonstrations with the PMT were carried out between 1 megabit-per-second (Mbps) and 8.7 Mbps at 7.8 meters, which represented between 8 and 12 beam extinction lengths. With the APD, 125 Mbps were demonstrated at 4.8 meters, representing approximately 5 extinction lengths.