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arXiv:quant-ph/0602158 · Optics Letters

Single-photon continuous-variable quantum key distribution based on the energy-time uncertainty relation

Bing Qi

Published Aug 25, 2006• 48 citations
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Abstract

We propose a new quantum key distribution protocol in which information is encoded on continuous variables of a single photon. In this protocol, Alice randomly encodes her information on either the central frequency of a narrowband single-photon pulse or the time delay of a broadband single-photon pulse, while Bob randomly chooses to do either frequency measurement or time measurement. The security of this protocol rests on the energy-time uncertainty relation, which prevents Eve from simultaneously determining both frequency and time information with arbitrarily high resolution. Since no interferometer is employed in this scheme, it is more robust against various channel noises, such as polarization and phase fluctuations.

DOI
10.1364/ol.31.002795

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We propose a new quantum key distribution protocol in which information is encoded on continuous variables of a single photon. In this protocol, Alice randomly encodes her information on either the central frequency of a narrowband single-photon pulse or the time delay of a broadband single-photon pulse, while Bob randomly chooses to do either frequency measurement or time measurement. The security of this protocol rests on the energy-time uncertainty relation, which prevents Eve from simultaneously determining both frequency and time information with arbitrarily high resolution. Since no interferometer is employed in this scheme, it is more robust against various channel noises, such as polarization and phase fluctuations.
A new scheme of quantum key distribution (QKD) using frequency and time coding is proposed, in which the security is based on the frequency-time uncertainty relation. In this scheme, the binary information sequence is encoded randomly on either the central frequency or the time delay of the optical pulse at the sender. The central frequency of the single photon pulse is set as ω 1 for bit 0 and set as ω 2 for bit 1 when frequency coding is selected. However, the single photon pulse is not delayed for bit 0 and is delayed in τ for 1 when time coding is selected. At the receiver, either the frequency or the time delay of the pulse is measured randomly, and the final key is obtained after basis comparison, data reconciliation and privacy amplification. With the proposed method, the effect of the noise in the fiber channel and environment on the QKD system can be reduced effectively.
We propose a quantum key distribution system based on the generation and transmission of random continuous variables in time, energy (frequency), phase, and photon number. The bounds for quantum measurement in our scheme are determined by the uncertainty principle, rather than single quadrature measurements of entangled states, or the no-cloning of (unknown) single quantum states. Correlated measurements are performed in the energy-time, and momentum-displacement frames. As a result the QKD protocols for generation of raw-keys, sifted-keys and privacy amplifications offer a higher level of security against individual or multi-attacks. The network architecture is in a plug-and-play configuration; the QKD protocol; determination of quantum bit error rate, and estimation of system performance in the presence of eavesdropping are presented.
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 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 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.