Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction

A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.Comment: 16 pages, 3 figures. Ver.4: Title changed. Ver.3: Due to a request of the AE of the journal, the present version has become a combination of (thoroughly revised) quant-ph/0610194 and the former quant-ph/0610195. Problem formulations of polynomial complexity are strictly followed. An erroneous instance of a lower bound on minimum distance was remove

Quantum information with continuous variables

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. We review the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.Comment: accepted for publication in Reviews of Modern Physic

Introduction to Quantum Information Processing

As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory, on developing new applications of quantum information and on physically realizing controllable quantum devices. The purpose of this primer is to provide an elementary introduction to quantum information processing, and then to briefly explain how we hope to exploit the advantages of quantum information. These two sections can be read independently. For reference, we have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at http://www.c3.lanl.gov/~knill/qip/prhtm

Depth-Bounded Quantum Cryptography with Applications to One-Time Memory and More

With the power of quantum information, we can achieve exciting and classically impossible cryptographic primitives. However, almost all quantum cryptography faces extreme difficulties with the near-term intermediate-scale quantum technology (NISQ technology); namely, the short lifespan of quantum states and limited sequential computation. At the same time, considering only limited quantum adversaries may still enable us to achieve never-before-possible tasks. In this work, we consider quantum cryptographic primitives against limited quantum adversaries - depth-bounded adversaries. We introduce a model for (depth-bounded) NISQ computers, which are classical circuits interleaved with shallow quantum circuits. Then, we show one-time memory can be achieved against any depth-bounded quantum adversaries introduced in the work, with their depth being any pre-fixed polynomial. Therefore we obtain applications like one-time programs and one-time proofs. Finally, we show our one-time memory has correctness even against constant-rate errors

A high-speed multi-protocol quantum key distribution transmitter based on a dual-drive modulator

We propose a novel source based on a dual-drive modulator that is adaptable and allows Alice to choose between various practical quantum key distribution (QKD) protocols depending on what receiver she is communicating with. Experimental results show that the proposed transmitter is suitable for implementation of the Bennett and Brassard 1984 (BB84), coherent one-way (COW) and differential phase shift (DPS) protocols with stable and low quantum bit error rate. This could become a useful component in network QKD, where multi-protocol capability is highly desirable.Comment: 15 pages, 7 figure