Raw Key Exchange

Thursday 11 June 2009

BB84 and SARG are two Quantum Key Distribution protocols based on the same qubits exchange procedure. It consists for one of the two parties in sending random qubits, and for the other party in measuring them. A qubit is a bit value coded using the property of a quantum particle. Different properties — such as the polarization or the phase of photons — can be used. As an illustration, polarization coding will be considered here.

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Polarization of Photons

Hence, an emitter and a receiver implement the Raw Key Exchange by exchanging single-photons, whose polarization states are used to encode bit values (refer to the Polarization of Photons figure for an explanation of the concept of polarization) over an optical fiber. This fiber, and the transmission equipment, is called the quantum channel. To implement the BB84 protocol, they use four different polarization states and agree, for example, that a 0-bit value can be encoded either as a horizontal state or a –45° diagonal one. For a 1-bit value, they will use either a vertical state or a +45° diagonal one. in the case of the SARG, the association between polarization and bit value is different, but they still use the same four polarization states.

Raw Key Exchange goes as follows:

  1. For each bit, the emitter sends a photon whose polarization is randomly selected among the four states. He records the orientation in a list.
  2. The photon is sent along the quantum channel.
  3. For each incoming photon, the receiver randomly chooses the orientation — horizontal or diagonal — of a filter allowing to distinguish between two polarization states. He records these orientations, as well as the outcome of the detections — photon deflected to the right or the left.
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Raw Key Exchange example

The Raw Key Exchange example figure illustrate a sequence of qubits exchange. By convention, the emitter is called Alice et the receiver is called Bob. For the first qubit exchanged, Alice sends a +45° polarization (bit value of 1) and Bob measures using the horizontal filter. He gets a bit value of 0. The second qubit sent by Alice is a 1 bit value encoded in the horizontal base (vertical polarization). Bob measures in the horizontal base, he gets a bit of 1. And so on for the other qubits.

After a large number of qubits have been sent, the raw bit list of the emitter corresponds to the list of bit values he has sent through the quantum channel. The raw bit list of the receiver is composed of the list of bit values he has measured. Notice that these two lists are different since their lengths are different. Indeed qubits do not always reach the receiver due to loss in the quantum channel. To extract a raw key from these raw bit lists, the receiver announces to the emitter the index of the qubits for which he had a detection. This announcement is made by classical communication. The two parties use then a Key Sifting procedure to obtain a sifted key from this raw key.

Readers interested in the optical platform used in the quantum layer of the SwissQuantum network should refer to the id Quantique’s optical platform: Plug-&-Play page.

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