High-dimensional quantum key distribution using dispersive optics

Jacob Mower, Zheshen Zhang, Pierre Desjardins, Catherine Lee, Jeffrey H. Shapiro, and Dirk Englund

Phys. Rev. A 87, 062322 – Published 20 June 2013

Abstract

We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against collective attacks. The protocol, which represents a QKD analog of pulse position modulation, is compatible with standard fiber telecommunications channels and wavelength division multiplexers. We describe several physical implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at $> 4$ bits per character of distilled key across over 200 km of fiber.

Received 21 March 2012

DOI:https://doi.org/10.1103/PhysRevA.87.062322

Authors & Affiliations

Jacob Mower^1,2, Zheshen Zhang¹, Pierre Desjardins³, Catherine Lee^1,4, Jeffrey H. Shapiro¹, and Dirk Englund^1,2,3

¹Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Electrical Engineering, Columbia University, New York, New York 10027, USA
³Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
⁴Department of Physics, Columbia University, New York, New York 10027, USA

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Vol. 87, Iss. 6 — June 2013

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Images

Figure 1
(a) Alice and Bob measure in either the time or dispersed-time basis. In case (1), Alice measures in the dispersed-time basis and projects Bob's photon onto a dispersed state. In case (2), she projects Bob's photon onto an undispersed state. Only measurements in the same basis are correlated. QC represents quantum communication and CC represents classical communication. (b) An equivalent prepare-and-measure scheme in which Alice uses the arrival time of one photon as a sync time sent to Bob. She selects with a switch (S) whether or not to apply dispersion on her other photon and modulates the center time of the distribution that she sends to Bob using a Gaussian-distributed random number generator.Reuse & Permissions
Figure 2
(left) Secret-key capacity as a function of channel length, assuming equal photon pair generation rate $γ_{ν} = p_{ν} / 6 σ_{c o h}$ and $σ_{c o h} = 64 \times 30$ ps for all $d$ ; propagation loss $α = 0.2$ dB/km; detector timing jitter $σ_{J} = 20$ ps; Alice and Bob system detection efficiencies $93 %$ ; $σ_{Δ} = 10$ ps; dark count rate, $r_{D} = 1000$ s $^{- 1}$ ; $β = 0.9$ ; expected number of pairs per frame assuming heralding, $p_{ν} = {0.607, 0.411, 0.231, 0.119}$ for $d = {64, 32, 16, 8}$ , respectively (see Appendix ). (right) The secret-key capacity given the same parameters, but with $γ_{ν} = p_{ν} / (6 d \cdot σ_{c o r})$ and $σ_{c o r} = 30$ ps for all $d$ . Upper plots show bps. Lower plots show bpc, i.e., bits per frame in which Alice and Bob measure in the same basis and register only one detection event.Reuse & Permissions
Figure 3
$Δ I$ as a function of offset parameter $σ_{Δ}$ assuming the parameters given in the caption of Fig. 2. (Left) Photon pair generation rate $γ_{ν} = p_{ν} / 6 σ_{c o h}$ and $σ_{c o h} = 64 \times 30$ ps for all $d$ . (Right) $γ_{ν} = p_{ν} / (6 d \cdot σ_{c o r})$ and $σ_{c o r} = 30$ ps for all $d$ .Reuse & Permissions
Figure 4
Prepare-and-measure scheme in which Alice additionally modulates the output channel according to the heralding scheme outlined in the text using the element Mod. Arrival-time measurements from her idler photon are fed forward to Mod enabling Alice to suppress multiphoton emission during each frame.Reuse & Permissions
Figure 5
(Upper) Probability of Alice sending one photon per frame to Bob, $p (1)$ , as a function of $μ_{f}$ using the heralding circuit with the $d$ shown and for unheralded $g$ -fold degenerate Bose-Einstein statistics “ $g$ -BE.” (Lower) The probability of Alice sending more than one photon per frame given that one or more photons were sent for the heralded and thermal statistics as above. We limit this probability to be less than $0.01$ , which places an upper bound on $μ_{f}$ .Reuse & Permissions

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