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[CrossRef]

A practical laser presents some classical noises, such as occupation fluctuations [26] and 1/f noise (see Electron. Lett., 19, 812, 1983). These classical noises are power independent [26].

To experimentally determine γ, the key idea is that when the laser is operated at a significant high power level, the classical noise part (C in Eq. (3)) will dominate over the quantum fluctuations part (QP in Eq. (3)). It consists of three steps: a) at an optical power level Po, we measured the variance of Vpr(t) as σ12. b) the laser was operated to its maximal power (around 25 mW for our DFB laser diode) and an optical attenuator (JDS Uniphase HA1) was applied right after the laser to attenuate the output power down to Po, in which the variance of Vpr(t) was measured as σ22. From σ12 and σ22, we could derive the experimental value γ=σ12−σ22σ22 at power Po. c) the process was repeated at different power levels and the experimental results were shown in Fig. 3.

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, under preparation (2011).

There are mainly five spikes around 0, 100, 200, 500, and 650 MHz. These frequencies are all within practical broadcast radio bands (see http://www.fcc.gov/oet/spectrum ).

To reduce the correlations and ensure the independence between adjacent samples, the sampling time (1 ns) has been chosen to be larger than the sum of PLC-MZI time difference (500 ps) and detector response time (200 ps). For details, see Ref. [19].

We remark that in a practical system, it will be interesting for future research to investigate how to determine an optimal ADC range, which can maximize the extractable randomness.

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[CrossRef]

For demonstration purpose, we use pseudo-random number generator of Matlab to generate the seed constructing Toeplitz matrix. In the future, we plan to generate the seed from either some well-developed QRNGs (such as Ref. [16]) or pre-stored random bits generated by our own QRNG system. Note that Toeplitz-hashing allows the re-use of the seed in subsequent applications (see details in [31]).

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