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arXiv:0705.1600

A mathematical criterion for single photon sources used in quantum cryptography

Anirban Pathak

Published May 11, 2007• 1 citation
arXivHTMLPDF

Abstract

A single photon source (SPS) is very important for quantum computation. In particular, it is essential for secured quantum cryptography. But there is no perfect SPS in reality. Therefore, probabilistic SPS where probability of simultaneous emission of two, three, four and more photon is less than the emission of a single photon are used. Since classical photon always comes in bunch, the required single photon source must be nonclassical. In the well-known antibunched state the rate of simultaneous emission of two photon is less than that of single photon. But the requirement of quantum cryptography is a multiphoton version of the antibunched state or the higher order antibunched state. Recently we have reported a mathematical criterion for higher order antibunching. Here we have shown that any proposal for SPS to be used in quantum cryptography should satisfy this criterion. We have studied four wave mixing as a possible candidate of single photon source.

DOI
10.48550/arxiv.0705.1600

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A single photon source (SPS) is very important for quantum computation. In particular, it is essential for secured quantum cryptography. But there is no perfect SPS in reality. Therefore, probabilistic SPS where probability of simultaneous emission of two, three, four and more photon is less than the emission of a single photon are used. Since classical photon always comes in bunch, the required single photon source must be nonclassical. In the well-known antibunched state the rate of simultaneous emission of two photon is less than that of single photon. But the requirement of quantum cryptography is a multiphoton version of the antibunched state or the higher order antibunched state. Recently we have reported a mathematical criterion for higher order antibunching. Here we have shown that any proposal for SPS to be used in quantum cryptography should satisfy this criterion. We have studied four wave mixing as a possible candidate of single photon source.
Abstract Single photon source for use in quantum cryptography should show higher order photon antibunching. We have analyzed non classical effect i.e. higher order photon antibunching in pump mode of eight-wave mixing non linear optical process using short time interaction technique and also the dependence of non classicality on the number of photons prior to interaction in non linear medium. Further we have reported that higher the order of photon antibunching, higher will be the probability to generate single photon source utilized in quantum cryptography.
Single photon sources to be used in quantum cryptography must show higher order antibunching (HOA). HOA is reported by us in several many wave mixing processes. In the present work we have investigated the possibility of observing HOA in multiwave mixing processes in general. The generalized Hamiltonian is solved for several particular cases in Heisenberg picture and possibility of observing HOA is investigated with the help of criterion of Pathak and Garcia. The generalized interaction Hamiltonian of a multiwave mixing process is considered as (a†l bm cn + Hermitian conjugate) where 'a', 'b' and 'c' are the annihilation operators corresponding to pump, Stokes and Signal modes respectively. Several particular cases of the generalized Hamiltonian are solved with the help of short time approximation technique and HOA is reported for pump modes of different multiwave mixing processes. It is also found that HOA can not be observed for the signal and stokes modes in of the cases studied here.
A single-photon source is a key advancement for quantum computing, quantum sensing, metrology, and quantum communication. These applications use single photons and have demanding standards for the effectiveness of single-photon generation. All available single photon source (SPS) is probabilistic and the search for deterministic SPS is challenging and relatively new. In this work, we explore a quantitative approach that can be applied to various sources with well-defined mathematical distribution functions in photon emission. If we have a photon number distribution, then we can easily compute the possibility of emission of a single photon from the source. Here, we observe the single photon possibility in a quantum state named as New Generalised Binomial State. Furthermore, this criterion has been applied to a single photon added New Generalised Binomial state and a single photon subtracted New Generalised Binomial State too. This technique helps us to characterize the quality of a single photon source. We explore the variation of SPS probability with different parameters and it is found that probability varies with the total number of photons in a system, the q parameter should be negative and the addition of a Photon is more suitable than subtraction for single photon source criterion.
Abstract Quantum cryptography harnesses quantum light, in particular single photons, to provide security guarantees that cannot be reached by classical means. For each cryptographic task, the security feature of interest is directly related to the photons’ non-classical properties. Quantum dot-based single-photon sources are remarkable candidates, as they can in principle emit deterministically, with high brightness and low multiphoton contribution. Here, we show that these sources provide additional security benefits, thanks to the tunability of coherence in the emitted photon-number states. We identify the optimal optical pumping scheme for the main quantum-cryptographic primitives, and benchmark their performance with respect to Poisson-distributed sources such as attenuated laser states and down-conversion sources. In particular, we elaborate on the advantage of using phonon-assisted and two-photon excitation rather than resonant excitation for quantum key distribution and other primitives. The presented results will guide future developments in solid-state and quantum information science for photon sources that are tailored to quantum communication tasks.
The first quantum cryptography protocol, proposed by Bennett and Brassard in 1984 (BB84), has been widely studied in recent years. This protocol uses four states (more precisely, two complementary bases) for the encoding of the classical bit. Recently, it has been noticed that by using the same four states, but a different encoding of information, one can define a protocol which is more robust in practical implementations, specifically when attenuated laser pulses are used instead of single-photon sources [V. Scarani et al., Phys. Rev. Lett. 92, 057901 (2004), referred to as the SARG04 protocol]. We present a detailed study of SARG04 in two different regimes. In the first part, we consider an implementation with a single-photon source: we derive bounds on the error rate QQQ for security against all possible attacks by the eavesdropper. The lower and the upper bound obtained for SARG04 ($Q\ensuremath{\lesssim}10.95%$ and $Q\ensuremath{\gtrsim}14.9%$, respectively) are close to those obtained for BB84 ($Q\ensuremath{\lesssim}12.4%$ and $Q\ensuremath{\gtrsim}14.6%$, respectively). In the second part, we consider a realistic source consisting of an attenuated laser and improve on previous analysis by allowing Alice to optimize the mean number of photons as a function of the distance. The SARG04 protocol is found to perform better than BB84, both in secret-key rate and in maximal achievable distance, for a wide class of Eve's attacks.
A reliable single photon source is a prerequisite for linear optical quantum computation and for secure quantum key distribution. A criterion yielding a conclusive test of the single photon character of a given source, attainable with realistic detectors, is therefore highly desirable. In the context of heralded single photon sources, such a criterion should be sensitive to the effects of higher photon number contributions, and to vacuum introduced through optical losses, which tend to degrade source performance. In this Rapid Communication we present, theoretically and experimentally, a criterion meeting the above requirements.