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Physical Review A

Time coding protocols for quantum key distribution

Thierry Debuisschert, William Boucher

Published Oct 8, 2004• 25 citations
Publisher

Abstract

We propose quantum key distribution protocols based on coherent single-photon optical pulses with duration $T$ and with minimum time-frequency uncertainty. The pulses are sent with possible delays (e.g., 0, $T∕2$) that are used to code the information (e.g., bit 0, bit 1) and that are shorter than the pulse width. Therefore, the time detection of the photons may result in a ambiguity of the delay evaluation for a potential eavesdropper. The duration of the received pulses is controlled thanks to a contrast measurement using an interferometer. A quantum formalism is given, allowing us to model the transmission of the key and the consequences of a possible eavesdropping. Two protocols are proposed and discussed. The first one involves two states and is limited to channels with losses lower than 50%. The second one involves four states, which prevents the eavesdropper from exploiting the losses of the line. The security of each protocol is evaluated as a function of channel losses, quantum bit error rate, and contrast loss in the case of intercept-resend attacks. It is applied to situations where photocounters dark counts are the main limitation of the system. The resulting maximum propagation distance allowing secure communication is evaluated.

DOI
10.1103/physreva.70.042306

Related papers

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We have implemented an experimental setup in order to demonstrate the feasibility of time-coding protocols for quantum key distribution. Alice produces coherent 20-ns faint pulses of light at 853 nm. They are sent to Bob with delay 0 ns (encoding bit 0) or 10 ns (encoding bit 1). Bob directs at random the received pulses to two different arms. In the first one, a 300 ps resolution Si photon counter allows Bob to precisely measure the detection times of each photon in order to establish the key. Comparing them with the emission times of the pulses sent by Alice allows one to evaluate the quantum bit error rate (QBER). The minimum obtained QBER is 1.62%. The possible loss of coherence in the setup can be exploited by Eve to eavesdrop the line. Therefore, the second arm of Bob setup is a Mach-Zehnder interferometer with a 10 ns propagation delay between the two paths. Contrast measurement of the output beams allows one to measure the autocorrelation function of the received pulses that characterizes their average coherence. In the case of an ideal setup, the value expected with the pulses sent by Alice is 0.576. The experimental value of the pulses autocorrelation function is found to be 0.541. Knowing the resulting loss of coherence and the measured QBER, one can evaluate the mutual information between Alice and Eve and the mutual information between Alice and Bob, in the case of intercept-resend attacks and in the case of attacks with intrication. With our values, Bob has an advantage on Eve of 0.43 bit per pulse. The maximum possible QBER corresponding to equal informations for Bob and Eve is 5.8%. With the usual attenuation of fibres at 850 nm, it shows that secure key distribution is possible up to a distance of 2.75 km, which is sufficient for local links.

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Optics and Spectroscopy•Mar 1, 2010•3 citations
We propose quantum key distribution protocols based on coherent single-photon optical pulses with duration TTT and with minimum time-frequency uncertainty. The pulses are sent with possible delays (e.g., 0, T∕2T∕2T∕2) that are used to code the information (e.g., bit 0, bit 1) and that are shorter than the pulse width. Therefore, the time detection of the photons may result in a ambiguity of the delay evaluation for a potential eavesdropper. The duration of the received pulses is controlled thanks to a contrast measurement using an interferometer. A quantum formalism is given, allowing us to model the transmission of the key and the consequences of a possible eavesdropping. Two protocols are proposed and discussed. The first one involves two states and is limited to channels with losses lower than 50%. The second one involves four states, which prevents the eavesdropper from exploiting the losses of the line. The security of each protocol is evaluated as a function of channel losses, quantum bit error rate, and contrast loss in the case of intercept-resend attacks. It is applied to situations where photocounters dark counts are the main limitation of the system. The resulting maximum propagation distance allowing secure communication is evaluated.
We have implemented an experimental setup in order to demonstrate the feasibility of time-coding protocols for quantum key distribution. Alice produces coherent 20-ns faint pulses of light at 853 nm. They are sent to Bob with delay 0 ns (encoding bit 0) or 10 ns (encoding bit 1). Bob directs at random the received pulses to two different arms. In the first one, a 300 ps resolution Si photon counter allows Bob to precisely measure the detection times of each photon in order to establish the key. Comparing them with the emission times of the pulses sent by Alice allows one to evaluate the quantum bit error rate (QBER). The minimum obtained QBER is 1.62%. The possible loss of coherence in the setup can be exploited by Eve to eavesdrop the line. Therefore, the second arm of Bob setup is a Mach-Zehnder interferometer with a 10 ns propagation delay between the two paths. Contrast measurement of the output beams allows one to measure the autocorrelation function of the received pulses that characterizes their average coherence. In the case of an ideal setup, the value expected with the pulses sent by Alice is 0.576. The experimental value of the pulses autocorrelation function is found to be 0.541. Knowing the resulting loss of coherence and the measured QBER, one can evaluate the mutual information between Alice and Eve and the mutual information between Alice and Bob, in the case of intercept-resend attacks and in the case of attacks with intrication. With our values, Bob has an advantage on Eve of 0.43 bit per pulse. The maximum possible QBER corresponding to equal informations for Bob and Eve is 5.8%. With the usual attenuation of fibres at 850 nm, it shows that secure key distribution is possible up to a distance of 2.75 km, which is sufficient for local links.
A new family of two-parameter quantum key distribution protocols is discussed where eavesdropping is detected by using two parameters: bit error rate Q and photon count rate q in control time slots. When a single-photon source is used and mutually orthogonal states are prepared in each basis, the protocol’s maximum tolerable error rate for secure key distribution is the highest, reaching a theoretical upper limit of 50%. When the signal states emitted by the source of attenuated laser light include multiphoton coherent states, the protocol also guarantees secure key distribution over the longest distance as compared to other quantum cryptography systems, up to the channel length for which the channel losses are sufficiently high that all five-photon pulses can be blocked by an eavesdropper.
We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows to detect eavesdropping of the key. We give a mathematical model of a first protocol from which we derive a second, simpler, protocol. We derive the security analysis of both protocols and find that the secure rates can be similar to those obtained with the BB84 protocol. We then calculate the secure distance for those protocols over standard fibre links. When using low-noise superconducting single photon detectors, secure distances over 200 km can be foreseen. Finally, we analyse the consequences of photon-number splitting attacks when faint pulses are used instead of single photon pulses. A decoy states technique can be used to prevent such attacks.
We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows to detect eavesdropping of the key. We give a mathematical model of a first protocol from which we derive a second, simpler, protocol. We derive the security analysis of both protocols and find that the secure rates can be similar to those obtained with the BB84 protocol. We then calculate the secure distance for those protocols over standard fibre links. When using low-noise superconducting single photon detectors, secure distances over 200 km can be foreseen. Finally, we analyse the consequences of photon-number splitting attacks when faint pulses are used instead of single photon pulses. A decoy states technique can be used to prevent such attacks.
Summary form only given. An alternative protocol to polarization coding or phase coding is proposed for quantum key distribution. It is based on a time coding technique which is expected to be robust against propagation medium disturbances. The information is coded on one photon pulses of duration T and with a chosen time delay with respect to a time reference. The possible delays are chosen by Alice so that possible pulses may overlap. Bob uses photon counters with a time resolution much better than the pulse duration and he measures the detection time with respect to the reference. He can perform only one measurement which may lead to an ambiguity on the delay evaluation.
We suggest a protocol for quantum key distribution—a technology allowing two distant parties to create an unconditionally secure cryptographic key. For the creation of the key we suggest to use laser pulses weakened to the single-photon level of duration T , the pulse carrying the value “1” being shifted in time by T /2 compared to the pulse carrying the value “0”. The overlap of the pulses provides their non-orthogonality and, therefore, impossibility to discriminate between them with certainty. Besides the signal pulses the protocol uses coherent decoy pulses, having longer duration than the signal ones and providing a more effective protection from a wide class of attacks. Security of the protocol is based on interferometric control of the pulse coherence at the receiving station. We analyze the security of the protocol against a number of intercept-resend attacks and on the basis of this analysis substantiate the necessity of decoy state implementation.