Quantum Cryptography Without Switching

We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.

Figure 1

(a) Schematic of the simultaneous quadrature measurement protocol. ${\mathcal{S}}^{\pm }$: random Gaussian numbers, AM: amplitude modulator, PM: phase modulator, ${\widehat{X}}_A^{\pm }$: quadratures of Alice’s prepared state, $\eta$: channel transmission, ${\widehat{N}}^{\pm }$: channel noise, ${\widehat{X}}_B^{\pm }$: observables that Bob measures and ${\widehat{N}}_B^{\pm }$: Bob’s vacuum noise. (b) Schematic of a possible feed forward attack for Eve. ${\widehat{X}}_E^{\pm }$: observables that Eve measures, ${\widehat{N}}_{E1}^{\pm }$ and ${\widehat{N}}_{E2}^{\pm }$: Eve’s vacuum noises, $g_E^{\pm }$: Eve’s electronic gains and ${\mathcal{N}}^{\pm }$: additional Gaussian noise.

Figure 2

Contour plot of the information rate for the simultaneous quadrature measurement protocol as a function of channel efficiency $\eta$ and channel noise $V_N$ in units of (bits/symbol) for $V_A=100$.

Figure 3

Net information rates for the simultaneous and single quadrature measurement schemes as a function of channel efficiency. (i) Dashed line, simultaneous quadrature measurement. (ii) Dotted-dashed line, single quadrature measurement. (iii) Solid line, simultaneous quadrature measurement with feed forward attack. For a variance of $V_A=100$ with varying channel noise: (a) ${\mathrm{V}}_N=1$, (b) $V_N=1.2$, and (c) $V_N=2$.

Figure 4

Information rates for the simultaneous and single quadrature measurement schemes as a function of channel efficiency $\eta$, with $V_A^{\pm }=100$ and $V_N^{\pm }=1$. The net information rate for both schemes is $\Delta I=I_{BA}-I_{BE}$. In the case of simultaneous quadrature measurements, $I_{BE}$, the dashed line, denotes maximum information rate obtained by Eve, while $I_{BE}^{ff}$, the dotted-dashed line, denotes the information rate obtained by Eve using the feed forward attack.