Measuring Linear Polarization of Real Photons

Bo Yu, Zhenqiang YIN, Weijie DING +2 more

The key security of quantum key distribution (QKD) is guaranteed by the basic principle of quantum mechanics, which makes it possible to combine information theory security communication with one-time encryption. The key is usually encoded on the polarization dimension or phase dimension of a single-photon. It is considered that the birefringence effect of single-mode fiber leads to a random variation of polarization state, which would induce the bit error rate. So it is of great significance to keep the single-photon linear polarization state stable for both polarization encoding QKD system and phase encoding QKD system. By using the single-photon polarization modulation technology, the single-photon linear polarization state periodically varies with the external modulation signal. The flicker noise is suppressed effectively, and the signal-to-noise ratio (SNR) of single-photon counting is increased as indicated by the phase-sensitive detection with a lock-in amplifier (LIA). The error signal is generated by demodulating the modulated single photons and it is used to lock an arbitrary 1550 nm single-photon linear polarization state to the optical axis of in-line polarizer (ILP). The modulation frequency reaches up to 5 kHz, which can eliminate the influence of low frequency flicker noise. The LIA demodulates the single-photon pulses by using 78.1 Hz filter bandwidth, with a time constant of 1 ms and a filter slope of 24 dB. The SNR of error signal is 20. The zero-crossing point of error signal represents the single photon’s linear polarization state aligned to the optical axis of ILP. The linear slope around the zero-crossing point for the polarization state angle versus the error signal amplitude is 1.267 rad/V. When the negative feedback loop does not work, the polarization drift of single-photon pulses is 0.082 rad due to the random environmental noise. However, by using the single-photon polarization modulation technology, the polarization drift of stable single-photon pulses is limited to 0.0011 rad within 2000 s through the precise control with a polarization rotator, and the corresponding Allan deviation reaches the minimal value of 6.7×10–5 at an integration time of 128 ms. The advantages for the single-photon polarization modulation technology are as follows: i) the linear polarization state drift is compensated in real-time at the single-photon level; ii) single frequency polarization modulation can be extended to multiple frequency polarization modulation in order to achieve simultaneous locking of multiple linear polarization states of single-photon pulses; iii) these 1550 nm single-photon pulses with the 0.0011 rad linear polarization state stability can be directly used as the single-photon source in either polarization encoding or phase encoding QKD system.

M. Iinuma

James M. Knight, Lev Vaidman A

Łukasz Michalik, Andrzej W. Domański

In this paper authors present a novel idea for reconstructing quantum states of polarized optical field expressed in the one-photon basis. The quantum state reconstruction is a measurement of a quasidistribution function P that allows to obtain a density operator for the analyzed state. The most commonly used approach for a quantum state reconstruction is based on the so called quantum tomography. The marginal probability distributions for the Wigner function are measured for different angles of projection and then they are put together into the two-dimensional distribution by the inverse Radon transformation. In our approach the analyzed field is combined with the reference field which is well defined, it can be for example a photon-beam containing linearly polarized photons only. The proposed thought experiment assumes that we measure the degree of linear polarization of this combined beam using a rotating polarizer. We obtain the searched distribution P by changing the parameters of the reference beam – its intensity and state of polarization. This series of measurements allows to build the system of equations The values of the function P at various points P(θ i, ϕ j) are the searched variables of this system. Accuracy of that solution depends on how many measurements are done.

Cody McKenzie, Preston Alexander, R. Seth Smith

A. Shafiee

We derive an efficient CH-type inequality. Quantum mechanics violates our proposed inequality independent of the detection-efficiency problem. In photonic Bell-type experiments [1], when photon pairs with parallel linear polarizations are emitted, one can consider a Clauser-Horne (CH) inequality [2], at the level of hidden variables, in the form where − 1 ≤ Srq,HV (â, ̂ b, â ′ , ̂ b ′ , λ) ≤ 0 (1) Srq,HV (â, ̂b, â ′ , ̂ b ′, λ) = p (1) r (â, λ) p (2) q (̂b, λ) − p (2) q ( ̂ b ′, λ)] +p (1) r ( â ′ , λ) [ p (2) q ( ̂b, λ) + p (2) q ( ̂ b ′, λ)] −p (1) r (â ′ , λ) − p (2) q ( ̂ b, λ) (2) In (2), we are considering four sub-ensemble of photon pairs with linear polarizations along (â, ̂ b), (â, ̂ b ′), ( â ′ , ̂ b), and ( â ′ , ̂ b ′ ) in which one registers