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arXiv:1207.5008

Quantum Key Distribution based on Single Photon Bi-partite Correlation

Kim Fook Lee, Yong Meng Sua, Harith Bin Ahmad

Published Jul 20, 2012• 1 citation
arXivHTMLPDF

Abstract

We present a scheme for key distribution based on bi-partite correlation of single photons. Alice keeps an ancilla photon and sends a signal photon to Bob, where intrinsic bi-partite correlation of these photons is obtained through first order intensity correlation in their detectors. The key bits are distributed through sharing four bi-partite correlation functions and photon counting. The scheme consists of two parts; first, Alice prepares deterministic photon states and Bob measures the photon states based on his random choice on correlation functions. Second, Alice guesses Bob's choice of correlation functions and sets the key bits by sending out photon states. Bob verifies the key bits through the photon states regardless Alice made a right or wrong guess. We called this key distribution scheme as prepare-measure-guess-verify (PMGV) protocol. We discuss the protocol by using a highly attenuated laser light, and then point out the advantages of using a fiber based correlated photon-pair to achieve better performance in security, communication distance and success rate of key distribution.

DOI
10.48550/arxiv.1207.5008

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We present a scheme for key distribution based on bi-partite correlation of single photons. Alice keeps an ancilla photon and sends a signal photon to Bob, where intrinsic bi-partite correlation of these photons is obtained through first order intensity correlation in their detectors. The key bits are distributed through sharing four bi-partite correlation functions and photon counting. The scheme consists of two parts; first, Alice prepares deterministic photon states and Bob measures the photon states based on his random choice on correlation functions. Second, Alice guesses Bob's choice of correlation functions and sets the key bits by sending out photon states. Bob verifies the key bits through the photon states regardless Alice made a right or wrong guess. We called this key distribution scheme as prepare-measure-guess-verify (PMGV) protocol. We discuss the protocol by using a highly attenuated laser light, and then point out the advantages of using a fiber based correlated photon-pair to achieve better performance in security, communication distance and success rate of key distribution.
A new conceptual key generation scheme is presented by using intrinsic quantum correlations of single photons between Alice and Bob. The intrinsic bi-partite correlation functions allow key bit to be generated through high level communication language i.e. a key bit is directly encoded to shared correlation functions not to the state and detection of a photon at Bob does not mean key bit. These make the scheme robust against intercept-resend attack because Alice and Bob can always check the errors in their measurements and reveal the presence of Eve in their channel without leaking any key bit information. The laser source is located in the middle of Alice and Bob, consists of two modes (x,y), relatively random phase-modulated (±π2)(\pm \fracπ{2})(±2π​) weak coherent states combined in a perfect 50/50 beam splitter. The scheme is strictly relied on the perfect beam splitter and mean photon number less than 1, where more than one photon in a coherent pulse will introduce more errors in Bob even without the presence of Eve. From the percentage of errors in Bob, we can estimate the amount of information will be leaked to Eve in the photon-number splitting attack. This scheme can preserve the randomness of phase-randomized light source for doubling the communication distance as in original Ekert's protocol and providing the raw key generation rate a factor of 2 higher than weak coherent light protocols.
A scheme for three-party quantum secret sharing of a private key is presented with single photons. The agent Bob first prepares a sequence of single photons with two biased bases and then sends them to the boss Alice who checks the security of the transmission with measurements and produces some decoy photons by rearranging the orders of some sample photons. Alice encodes her bits with two unitary operations on the photons and then sends them to the other agent. The security of this scheme is equivalent to that in the modified Bennett–Brassard 1984 quantum key distribution protocol. Moreover, each photon can carry one bit of the private key and the intrinsic efficiency for qubits and the total efficiency both approach the maximal value 100% when the number of the bits in the key is very large.
We propose a cryptographic scheme that is deterministic: Alice sends single photons to Bob, and each and every photon detected supplies one key bit—no photon is wasted. This is in marked contrast to other schemes in which a random process decides whether the next photon sent will contribute to the key or not. The determinism is achieved by preparing the photons in two-qubit states, rather than the one-qubit states used in conventional schemes. In particular, we consider the realistic situation in which one qubit is the photon polarization and the other a spatial alternative. Further, we show how one can exploit the deterministic nature for direct secure communication, that is without the need for establishing a shared key first.
Abstract Ideal quantum key distribution (QKD) protocols require perfect single photon sources, detectors, and lossless channels. However, the present technology cannot ensure all of the requirements. Among the variants of practical QKD schemes, decoy state QKD in its present form approaches nearly the theoretical security. In any decoy state method, a compromise is made between the security of the key distribution and the rate of key generation by optimizing the two major protocol parameters: the number of decoy states and their relative intensities, and the length of the data string as well. Use of more number of decoy states and higher range of intensities though improve security, their optimization becomes too complex. Therefore, from practical consideration, some restrictions are to be imposed on the choice of decoy states and their intensities. In addition, the treatment of correlations among the laser pulses in security analysis is not fully understood. Normally, lack of correlations or randomness among the signal states is considered to gain security, but, in a different approach, described in the proposed protocol, additional correlation is introduced to improve key generation rate without compromising security. To do that, a one-way function is shared among the legitimate users to provide a semi-random choice of bases depending on the outcome of the receiver’s detector. The initial communication is made through a set of bits with predefined bases and intensity distribution. Then, with the help of the positive outcome of the receiver’s detector, the basis set as well as the length of the bit string for subsequent communications are computed. This results in correlation among the bases and the relative intensities of the signal states and provides a self-checking mechanism to identify eavesdropping. The security analysis of the protocol provides a low error rate and a relatively high key generation rate.
We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states.