Quantum Coin: Difference between revisions
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* '''Quantum coin Verification''' - To verify a quantum coin through classical communication with the TTP, its holder sends the identification number of the quantum coin to the TTP. Then, the TTP and the coin holder exchange some classical information for choosing some quantum registers. The coin holder measures the chosen registers and sends their corresponding classical information to the TTP. The TTP verifies the authenticity of the coin by the secret information he possesses. | * '''Quantum coin Verification''' - To verify a quantum coin through classical communication with the TTP, its holder sends the identification number of the quantum coin to the TTP. Then, the TTP and the coin holder exchange some classical information for choosing some quantum registers. The coin holder measures the chosen registers and sends their corresponding classical information to the TTP. The TTP verifies the authenticity of the coin by the secret information he possesses. | ||
==Notations== | ==Notations== | ||
* <math>HMP_4</math>-states: <math>|\alpha(x)\rangle=\dfrac{1}{2}\sum_{1\leq i\leq4}(-1)^{x_i}|i\rangle</math>, <math>x\in\{0, 1\}</math> | * <math>HMP_4</math>-states: <math>|\alpha(x)\rangle=\dfrac{1}{2}\sum_{1\leq i\leq4}(-1)^{x_i}|i\rangle</math>, <math>x\in\{0, 1\}^4</math> | ||
* for <math>m, a, b \in \{0, 1\}</math>, <math>(x, m, a, b) \in HMP_4 </math> if <math> b = \begin{cases} | |||
x_1 \oplus x_{2+m} & \text{if } a = 0 \\ | |||
x_{3-m} \oplus x_4 & \text{if } a = 1 \end{cases}</math> | |||
* <math>HMP_4</math>-queries: An <math>HMP_4</math>-query is an element <math>m \in \{0, 1\}</math>. A valid answer to the query w.r.t. <math>x \in \{0, 1\}^4</math> is a pair <math>(a, b) \in \{0, 1\} \times \{0, 1\}</math>, such that <math>(x, m, a, b) \in HMP_4</math>. An <math>HMP_4</math> -state can be used to answer an <math>HMP_4</math> -query with certainty: If <math> m = 0 </math>, let | * <math>HMP_4</math>-queries: An <math>HMP_4</math>-query is an element <math>m \in \{0, 1\}</math>. A valid answer to the query w.r.t. <math>x \in \{0, 1\}^4</math> is a pair <math>(a, b) \in \{0, 1\} \times \{0, 1\}</math>, such that <math>(x, m, a, b) \in HMP_4</math>. An <math>HMP_4</math> -state can be used to answer an <math>HMP_4</math> -query with certainty: If <math> m = 0 </math>, let | ||
<math> v_1 \overset{def}{=}\dfrac{|1\rangle+|2\rangle}{\sqrt{2}} </math> <math> v_2 \overset{def}{=}\dfrac{|1\rangle-|2\rangle}{\sqrt{2}} </math> <math> v_3 \overset{def}{=}\dfrac{|3\rangle+|4\rangle}{\sqrt{2}} </math> <math> v_4 \overset{def}{=}\dfrac{|3\rangle-|4\rangle}{\sqrt{2}} </math> | <math> v_1 \overset{def}{=}\dfrac{|1\rangle+|2\rangle}{\sqrt{2}} </math> <math> v_2 \overset{def}{=}\dfrac{|1\rangle-|2\rangle}{\sqrt{2}} </math> <math> v_3 \overset{def}{=}\dfrac{|3\rangle+|4\rangle}{\sqrt{2}} </math> <math> v_4 \overset{def}{=}\dfrac{|3\rangle-|4\rangle}{\sqrt{2}} </math> | ||