# Encoding information on photon qubit

I study QKD which relies on the single photon as a qubit, on which information is encoded.

There are many protocols which mainly differ on how information (bit) is encoded on the qubit :

• polarization encoding
• frequency encoding
• time bin encoding
• phase encoding

I understand well polarization (or may I say spin/helicity encoding) of the single photon as it is a two levels system that can be represented by a qubit ($$|q\rangle = \alpha |0\rangle + \beta |1\rangle$$).

The three others are less clear for me.

For phase encoding, is it the phase ($$\gamma$$) of the photon as a qubit ($$|q\rangle = \cos (\theta / 2)|0\rangle + e^{i\gamma}\sin (\theta / 2)|1\rangle$$) ? or the phase between electrical field $$x$$ and $$y$$ components (which is related to light polarization) ?

For time bin (used in BB84 decoy state protocol) and frequency encodings, my question is does it still use any quantum properties ? i.e. that the photon be in a superposition of two states and, what are those states ? for time bin, is it that the photon be in one time bin or another (or both) and, for frequency, is it that the photon be in a particular frequency or both (??) ?

• If you use phase encoding, how to you measure the phase of a photon? Mar 25 at 1:38
• Yes, measuring the phase of a qubit is not impossible but difficult. I think phase and frequency encoding are related to Continuous Variable QKD which relies on the continous wave properties of light and you can measure the phase of light (phase shift between the two orthogonal components of electric field) Mar 27 at 20:34
• Phase refers to $\delta$. $x$ and $y$ are the parameters in phase space. It'd be good if you can give a reference about phase encoding. Mar 28 at 21:08
• Phase refers to $\delta$. $x$ and $y$ are the parameters in phase space. The encoding techniques, I belive, relate to those used in communication: polarization, frequency and phase modulations; time bins are used in many ways including CDMA and time-division multiplexing. It'd be good if you can give references on the time-bin and phase encodings. Mar 28 at 21:19