Editing Quantum Coin (section)

==Protocol Description==
'''Stage 1: Quantum coin generation'''<br>
''Input'': A secret record consists of <math>k</math> entries <math>x_1, . . . , x_k</math>,<math> x_i\in \{0,1\}^4</math><br>
''Output'': A “fresh” quantum coin<br>
The Trusted Third Party (TTP) chooses <math>x_1, . . . , x_k\in\{{0, 1}\}^4</math> at random, keeps them in secret and produces quantum states <math>|\alpha(x_1)\rangle, . . . , |\alpha(x_k)\rangle</math>. 
A “fresh” quantum coin corresponding to this record consists of:
* <math>k</math> quantum registers consisting of 2 qubits each, where the <math>i</math>-th register contains <math>|\alpha(x_i)\rangle</math>;
* a <math>k</math>-bit classical register <math>P</math>, that is initially set to <math>0^k</math>;
* a unique identification number.

'''Stage 2: Quantum coin verification'''<br>
''Input'': the identification number of the quantum coin<br>
''Output'': Accept or Reject<br>
<br>
This stage is run as follows:
* The holder sends the identification number of the quantum coin to the TTP.
* The TTP chooses uniformly at random a set <math>L_{bn}\subset[k]</math> of size <math>t</math>, and sends it to the coin holder.
* The holder consults with <math>P</math> and chooses uniformly at random a set <math>L_{hl} \subset L_{bn}</math> consisting of <math>2t/3</math> yet unmarked positions. He sends <math>L_{hl}</math> to the bank and marks in <math>P</math> all the elements of <math>L_{hl}</math> as used.
* The TTP chooses at random <math>2t/3</math> values <math>m_i \in\{{0, 1}\}</math>, one for each <math>i \in L_{hl}</math> , and sends them to the coin holder.
* The holder measures the quantum registers corresponding to the elements of <math>L_{hl}</math> in order to produce <math>2t/3</math> pairs <math>(a_i, b_i)</math> (refer to <math>HMP_4</math>-queries in Notations), such that <math>(x_i,m_i, a_i, b_i)\in HMP_4</math> for all <math>i \in L_{hl}</math>. He sends the list of <math>(a_i, b_i)</math>s to the TTP.
* The TTP checks whether <math>(x_i,m_i, a_i, b_i)\in HMP_4</math> for all <math>i \in L_{hl}</math>, in which case it confirms validity of the quantum coin. Otherwise, the coin is declared to be a counterfeit.