Unambiguous state discrimination in quantum cryptography with weak coherent states

The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor to some extend the photon number statistics of the signals even with todays standard detection schemes. We compare our attack to the beamsplitting attack and show that security against beamsplitting attack does not necessarily imply security against the attack considered here.Comment: 10 pages, 6 figures, updated version with added discussion of beamsplitting attac

Unambiguous State Discrimination of Coherent States with Linear Optics: Application to Quantum Cryptography

We discuss several methods for unambiguous state discrimination of N symmetric coherent states using linear optics and photodetectors. One type of measurements is shown to be optimal in the limit of small photon numbers for any N. For the special case of N=4 this measurement can be fruitfully used by the receiving end (Bob) in an implementation of the BB84 quantum key distribution protocol using faint laser pulses. In particular, if Bob detects only a single photon the procedure is equivalent to the standard measurement that he would have to perform in a single-photon implementation of BB84, if he detects two photons Bob will unambiguously know the bit sent to him in 50% of the cases without having to exchange basis information, and if three photons are detected, Bob will know unambiguously which quantum state was sent.Comment: 5 RevTeX pages, 2 eps figure

Security against eavesdropping in quantum cryptography

In this article we deal with the security of the BB84 quantum cryptography protocol over noisy channels using generalized privacy amplification. For this we estimate the fraction of bits needed to be discarded during the privacy amplification step. This estimate is given for two scenarios, both of which assume the eavesdropper to access each of the signals independently and take error correction into account. One scenario does not allow a delay of the eavesdropper's measurement of a measurement probe until he receives additional classical information. In this scenario we achieve a sharp bound. The other scenario allows a measurement delay, so that the general attack of an eavesdropper on individual signals is covered. This bound is not sharp but allows a practical implementation of the protocol.Comment: 11 pages including 3 figures, contains new results not contained in my Phys. Rev. A pape

Oscillator model for dissipative QED in an inhomogeneous dielectric

The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantised electric field is completely determined by the sources of the reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.Comment: 24 pages, 1 figur

Security against individual attacks for realistic quantum key distribution

I prove the security of quantum key distribution against individual attacks for realistic signals sources, including weak coherent pulses and downconversion sources. The proof applies to the BB84 protocol with the standard detection scheme (no strong reference pulse). I obtain a formula for the secure bit rate per time slot of an experimental setup which can be used to optimize the performance of existing schemes for the considered scenario.Comment: 10 pages, 4 figure

Quantum Cryptography with Coherent States

The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a new system, based on a symbiosis of two existing ones, and for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.Comment: 20 pp. Revtex, Figures available from the authors upon request, To be published in PRA (March 95

Design of a speed meter interferometer proof-of-principle experiment

The second generation of large scale interferometric gravitational wave detectors will be limited by quantum noise over a wide frequency range in their detection band. Further sensitivity improvements for future upgrades or new detectors beyond the second generation motivate the development of measurement schemes to mitigate the impact of quantum noise in these instruments. Two strands of development are being pursued to reach this goal, focusing both on modifications of the well-established Michelson detector configuration and development of different detector topologies. In this paper, we present the design of the world's first Sagnac speed meter interferometer which is currently being constructed at the University of Glasgow. With this proof-of-principle experiment we aim to demonstrate the theoretically predicted lower quantum noise in a Sagnac interferometer compared to an equivalent Michelson interferometer, to qualify Sagnac speed meters for further research towards an implementation in a future generation large scale gravitational wave detector, such as the planned Einstein Telescope observatory.Comment: Revised version: 16 pages, 6 figure

Entanglement of coherent states and decoherence

A possibility to produce entangled superpositions of strong coherent states is discussed. A recent proposal by Howell and Yazell [Phys. Rev. A 62, 012102 (2000)] of a device which entangles two strong coherent coherent states is critically examined. A serious flaw in their design is found. New modified scheme is proposed and it is shown that it really can generate non-classical states that can violate Bell inequality. Moreover, a profound analysis of the effect of losses and decoherence on the degree of entanglement is accomplished. It reveals the high sensitivity of the device to any disturbances and the fragility of generated states

Conditional beam splitting attack on quantum key distribution

We present a novel attack on quantum key distribution based on the idea of adaptive absorption [calsam01]. The conditional beam splitting attack is shown to be much more efficient than the conventional beam spitting attack, achieving a performance similar to the, powerful but currently unfeasible, photon number splitting attack. The implementation of the conditional beam splitting attack, based solely on linear optical elements, is well within reach of current technology.Comment: Submitted to Phys. Rev.

Local-Oscillator Noise Coupling in Balanced Homodyne Readout for Advanced Gravitational Wave Detectors

The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum back-action noise. Several back-action evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in table-top quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.Comment: 7 pages, 5 figure