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Optics and Spectroscopy

Optimization of optical fiber parameters to reduce errors of quantum key distribution using entangled polarization states of biphotons

George P. Miroshnichenko, A. A. Sotnikova

Published Mar 1, 2012• 3 citations
Publisher

Abstract

A phenomenological Hamiltonian of photons in single-mode stochastic fiber depending on the vector of random parameters is proposed. The time dynamics of single-photon density matrix in the basis of states with orthogonal polarizations is considered. The fiber-parameter-averaged quantum bit error rate (QBER) in a sifted quantum key distributed over the BB84 protocol using entangled polarization states of biphotons is found. It is shown that QBER can be significantly reduced even at large dispersions of random fiber parameters. To this end, identically fabricated fibers must be used for quantum channels A and B. The choice of pairs of fiber segments must be correlated, with a correlation coefficient close to unity. This approach is based on a remarkable property of the singlet biphoton state, which is “free of collective decoherence.” A correlated choice of fiber segments for channels A and B reduces significantly QBER, making its value below critical (i.e., equal to 0.11, a level below which a distributed key is accepted for cryptographic purposes).

DOI
10.1134/s0030400x12030137

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A phenomenological Hamiltonian of photons in single-mode stochastic fiber depending on the vector of random parameters is proposed. The time dynamics of single-photon density matrix in the basis of states with orthogonal polarizations is considered. The fiber-parameter-averaged quantum bit error rate (QBER) in a sifted quantum key distributed over the BB84 protocol using entangled polarization states of biphotons is found. It is shown that QBER can be significantly reduced even at large dispersions of random fiber parameters. To this end, identically fabricated fibers must be used for quantum channels A and B. The choice of pairs of fiber segments must be correlated, with a correlation coefficient close to unity. This approach is based on a remarkable property of the singlet biphoton state, which is “free of collective decoherence.” A correlated choice of fiber segments for channels A and B reduces significantly QBER, making its value below critical (i.e., equal to 0.11, a level below which a distributed key is accepted for cryptographic purposes).
A phenomenological Hamiltonian of photons in a single-mode stochastic inhomogeneous optical fiber (OF) is derived. Quantization of radiation is performed in the basis of an ideal OF with proper calibration that ensures transversality of the electric-field-displacement vector. Stochastic parameters of the Hamiltonian are determined by using the reciprocal tensor of the dielectric permittivity averaged over the OF segment volume. The Hamiltonian is parametrized by three phenomenological parameters and preserves the number of photons. It is assumed that the segment of the OF is divided into random subsegments with optical parameters defined by the Wiener process with respect to the longitudinal coordinate. The temporal dynamics of the single-photon density matrix is analyzed in the basis of states with orthogonal polarizations. The relative quantum beat error rate in the sifted quantum key distributed according to the BB84 protocol with polarization coding of information averaged over the scatter of the OF parameters is calculated.
In this work we consider the Liouville equation; it describes the dynamics of the photon density matrix in the Schr\"odinger representation based on the Markov approximation in the channel without dispersion. The equation contains a relaxation superoperator dependent on the phenomenological parameters of the optical fiber. These parameters allow one to take into account the phenomena of birefringence and optical activity, isotropic absorption, and dichroism. We also present in our work that these parameters affect not only the polarization of the states but the length of the Stokes vector. Hence the developed technique describes the decoherence process in the polarization domain in the quantum case and allows one to analyze the dynamics of single-photon states in the quantum (depolarizing) channel more properly. We also present a visual illustration of polarization states' evolution in the polarization-coded quantum key distribution BB84 protocol as an example. We estimate quantum bit error rates' dependence on channel length. Also we examine maximal allowed channel length, dependent on various configurations of channel parameters.
Affected by PMD(Polarization Mode Dispersion),the polarization state of the single photon will be randomly and slowly altered during the transmission in the fiber.This increases the error probability at the receiving end.So a means for measuring the variance to the preprocess polarization state is required for the distribution of the quantum key.A sensor with balanced detection is introduced to the BB84 protocol and the theoretical model of the QBER(Quantum Bit Error Rate) is established with POVM(Positive Operator Valued Measurement).The variance of the polarization state is measured with the Wollaston prism and the error is eliminated for the dual channel.The angle tolerance of the Wollaston prism is 0.1° and the numerical analysis by the use of the QBER model shows the new protocol decreases the error rate to 3.05×10-6.
Long-term quantum key distribution (QKD) using polarization encoding requires a random drift compensation method. We propose a method to compensate any state of polarization based on the quantum bit error rate (QBER) of two states from two non-orthogonal mutually unbiased bases. The proposed method does not require dedicated equipment, and through a simple but highly efficient feedback loop it compensates the polarization random drift suffered by photons while transmitted over the optical fiber quantum channel. A QBER lower than 2% was observed even considering imperfect single photon detectors. Besides, we verify a 82% secret key rate generation improvement in a finite-key size BB84 implementation for a 40 km fiber-optics quantum channel.
In this work, we represent the principle of quantum cryptography (QC) that is based on fundamental laws of quantum physics.QC or Quantum Key Distribution (QKD) uses various protocols to exchange a secret key between two communicating parties.This research paper focuses and examines the quantum key distribution by using the protocol BB84 in the case of encoding on the single-photon polarization and shows the influence of optical components parameters on the quantum key distribution.We also introduce Quantum Bit Error Rate (QBER) to better interpret our results and show its relationship with the intrusion of the eavesdropper called Eve on the optical channel to exploit these vulnerabilities.
The calibration of the polarization basis between the transmitter and receiver is an important task in quantum key distribution. A continuously working polarization-basis tracking scheme (PBTS) will effectively promote the efficiency of the system and reduce the potential security risk when switching between the transmission and calibration modes. Here, we proposed a single-photon level continuously working PBTS using only sifted key bits revealed during an error correction procedure, without introducing additional reference light or interrupting the transmission of quantum signals. We applied the scheme to a polarization-encoding BB84 QKD system in a 50 km fiber channel, and obtained an average quantum bit error rate (QBER) of 2.32% and a standard derivation of 0.87% during 24 h of continuous operation. The stable and relatively low QBER validates the effectiveness of the scheme.