Photon-Number-Splitting versus Cloning Attacks in Practical Implementations of the Bennett-Brassard 1984 protocol for Quantum Cryptography

In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs better than those described before. Using it, we confirm that, in the presence of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS. However, this improvement is very small for the implementations of the Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks is conceptually interesting but basically does not change the value of the security parameters of BB84. The main results are valid both for Poissonian and sub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde

Encoding a qubit in an oscillator

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested by Phys. Rev. A, minor correction

Quantum error-correcting codes associated with graphs

We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.Comment: 8 pages revtex, 5 figure

Topological Protection and Quantum Noiseless Subsystems

Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to quantum information processing is a particular instance of the notion of computation in a noiseless quantum subsystem. The latter then provide the most general conceptual framework for stabilizing quantum information and for preserving quantum coherence in topological and geometric systems.Comment: 4 Pages LaTeX. Published versio

Gigahertz quantum key distribution with InGaAs avalanche photodiodes

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.Comment: 4 pages, 4 figure

Simple Quantum Error Correcting Codes

Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where C_1 and C_2 are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing C_1 to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error correcting codes for 3, 4 and 5 information qubits with block lengths of 8, 10 and 11 qubits respectively.Comment: Submitted to Phys. Rev. A. in May 1996. 21 pages, no figures. Further information at http://eve.physics.ox.ac.uk/ASGhome.htm

Classicality in discrete Wigner functions

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.Comment: 10 pages, 1 figur

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.Comment: 5 pages, 4 figures, RevTe

Teleportation via thermally entangled state of a two-qubit Heisenberg XX chain

We find that quantum teleportation, using the thermally entangled state of two-qubit Heisenberg XX chain as a resource, with fidelity better than any classical communication protocol is possible. However, a thermal state with a greater amount of thermal entanglement does not necessarily yield better fidelity. It depends on the amount of mixing between the separable state and maximally entangled state in the spectra of the two-qubit Heisenberg XX model.Comment: 5 pages, 1 tabl

Mirax: A Brazilian X-Ray Astronomy Satellite Mission

We describe the ``Monitor e Imageador de Raios-X'' (MIRAX), an X-ray astronomy satellite mission proposed by the high energy astrophysics group at the National Institute for Space Research (INPE) in Brazil to the Brazilian Space Agency. MIRAX is an international collaboration that includes, besides INPE, the University of California San Diego, the University of Tuebingen in Germany, the Massachusetts Institute of Technology and the Space Research Organization Netherlands. The payload of MIRAX will consist in two identical hard X-ray cameras (10 -200 keV) and one soft X-ray camera (2-28 keV), both with angular resolution of ~ 5-6 arcmin. The basic objective of MIRAX is to carry out continuous broadband imaging spectroscopy observations of a large source sample (~ 9 months/yr) in the central Galactic plane region. This will allow the detection, localization, possible identification, and spectral/temporal study of the entire history of transient phenomena to be carried out in one single mission. MIRAX will have sensitivities of ~ 5 mCrab/day in the 2-10 keV band (~2 times better than the All Sky Monitor on Rossi X-ray Timing Explorer) and 2.6 mCrab/day in the 10-100 keV band (~40 times better than the Earth Occultation technique of the Burst and Transient Source Experiment on the Compton Gamma-Ray Observatory). The MIRAX spacecraft will weigh about 200 kg and is expected to be launched in a low-altitude (~ 600 km) circular equatorial orbit around 2007/2008.Comment: 6 pages, 1 table, 3 figures, presented at 2002 COSPAR meeting in Houston. Submitted to Adv. Space Re