All-optical logic circuits based on polarization properties of nondegenerate four-wave mixing

All-optical logic circuits based on the polarization properties of nondegenerate four-wave mixing are proposed. Schemes to perform multiple triple-product logic functions are discussed, and it is shown that higher-level Boolean operations that involve several bits can be implemented without resorting to the standard two-input gates. As a simple illustration of the idea, a circuit that performs error correction on a (3, 1) Hamming code is demonstrated. Error-free performance (bit error rate of <10^(−9)) at 2.5 Gbit/s is achieved after single-error correction on the Hamming word with 50% errors

Magic state distillation with punctured polar codes

We present a scheme for magic state distillation using punctured polar codes. Our results build on some recent work by Bardet et al. (ISIT, 2016) who discovered that polar codes can be described algebraically as decreasing monomial codes. Using this powerful framework, we construct tri-orthogonal quantum codes (Bravyi et al., PRA, 2012) that can be used to distill magic states for the $T$ gate. An advantage of these codes is that they permit the use of the successive cancellation decoder whose time complexity scales as $O(N\log(N))$. We supplement this with numerical simulations for the erasure channel and dephasing channel. We obtain estimates for the dimensions and error rates for the resulting codes for block sizes up to $2^{20}$ for the erasure channel and $2^{16}$ for the dephasing channel. The dimension of the triply-even codes we obtain is shown to scale like $O(N^{0.8})$ for the binary erasure channel at noise rate $0.01$ and $O(N^{0.84})$ for the dephasing channel at noise rate $0.001$. The corresponding bit error rates drop to roughly $8\times10^{-28}$ for the erasure channel and $7 \times 10^{-15}$ for the dephasing channel respectively.Comment: 18 pages, 4 figure

Optimum detection for extracting maximum information from symmetric qubit sets

We demonstrate a class of optimum detection strategies for extracting the maximum information from sets of equiprobable real symmetric qubit states of a single photon. These optimum strategies have been predicted by Sasaki et al. [Phys. Rev. A{\bf 59}, 3325 (1999)]. The peculiar aspect is that the detections with at least three outputs suffice for optimum extraction of information regardless of the number of signal elements. The cases of ternary (or trine), quinary, and septenary polarization signals are studied where a standard von Neumann detection (a projection onto a binary orthogonal basis) fails to access the maximum information. Our experiments demonstrate that it is possible with present technologies to attain about 96% of the theoretical limit.Comment: 10 pages, 11 figures, to be submitted to Phys. Rev. A Converted to REVTeX4 format, and a few other minor modifications according to the comments from PRA referre

Low-noise microwave polarimeter

Two quarterwave-plate polarizers inserted between rotary waveguide joints transform received signals from arbitrary linear to circular polarizations and then from circular to fixed linear polarizations. Fixed linear polarizations are applied to amplifiers and filters in usual fashion

Space-Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels

Slow fading broadcast channels can model a wide range of applications in wireless networks. Due to delay requirements and the unavailability of the channel state information at the transmitter (CSIT), these channels for many applications are non-ergodic. The appropriate measure for designing signals in non-ergodic channels is the outage probability. In this paper, we provide a method to optimize STBCs based on the outage probability at moderate SNRs. Multilevel polar coded-modulation is a new class of coded-modulation techniques that benefits from low complexity decoders and simple rate matching. In this paper, we derive the outage optimality condition for multistage decoding and propose a rule for determining component code rates. We also derive an upper bound on the outage probability of STBCs for designing the set-partitioning-based labelling. Finally, due to the optimality of the outage-minimized STBCs for long codes, we introduce a novel method for the joint optimization of short-to-moderate length polar codes and STBCs

Code diversity in multiple antenna wireless communication

The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gains. This geometric approach leads to remarkable examples, such as perfect space-time block codes, for which the complexity of Maximum Likelihood (ML) decoding is considerable. Code diversity is an alternative and complementary approach where a small number of feedback bits are used to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. This method of feedback provides gains associated with beamforming while minimizing the number of feedback bits. It complements the standard approach to code design by taking advantage of different (possibly equivalent) realizations of a particular code design. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal as shown for 4 by 4 Quasi-Orthogonal Space-Time Block Code (QOSTBC) and multi-user detection using the Alamouti code. Code diversity implemented by selecting from equivalent variants is used to improve ML decoding performance of the Golden code. This paper introduces a family of full rate circulant codes which can be linearly decoded by fourier decomposition of circulant matrices within the code diversity framework. A 3 by 3 circulant code is shown to outperform the Alamouti code at the same transmission rate.Comment: 9 page