Prepare-and-Send Verifiable Universal Blind Quantum Computation: Difference between revisions

Prepare-and-Send Verifiable Universal Blind Quantum Computation (edit)

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 * <math>|+\rangle_{\theta_i}</math>:  <math>\frac{1}{\sqrt{2}} (|0\rangle +e^{i\theta_i}|1\rangle)</math>
 * <math>\phi_i</math>: True measurement angle for qubit <math>i</math>.
-* <math>\phi^{'}_i</math>: Updated version of measurment angle for qubit <math>i</math>.
 * <math>r \in \{ 0, 1\}</math>: randomly chosen parameter for <math>\pi</math> rotation in order to hide classical output.
+* <math>\theta^{'}_i</math>: Updated version of Random local phase angle for qubit <math>i</math>.
 * <math>\delta_i</math>: Final measurement angle for qubit <math>i</math>.
 * <math>b_i</math>: Measurement output by the server.
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 * The client prepares <math>|e\rangle = X^{x1}_1 Z_1(\theta_1) \otimes ... \otimes X^{xn}_n Z_n(\theta_n)|I\rangle</math> using QOTP.
 * Client randomly chooses <math>t</math>, where <math>t \in D</math>.
-* For <math>i = n+1, n+2, ....m</math>:
+* For <math>i = n+1, n+2, ....m</math> (non-input qubits):
 ** if <math>i \in D</math>:
-*** if <math>i != t</math> then state <math>|0\rangle</math> or <math>|1\rangle</math> is prepared
+*** if <math>i  != t</math> then state <math>|0\rangle</math> or <math>|1\rangle</math> is prepared
 *** if <math>i == t</math> then <math>|+\rangle_{\theta_i}</math> is prepared
-** if <math>i</math> == non-input qubit then <math>|+\rangle_{\theta_i}</math> is prepared
+** else <math>|+\rangle_{\theta_i}</math> is prepared
-* For <math>l = 1, 2, ...n</math>:
+* <math>\forall l\epsilon\{1,..,n\}</math>, Client sends all qubits to server.
-** The client sends the qubits to the server.
 '''Stage 2: '''Server's preparation:</br>
-'''Output''': Cylinder brickwork state which has a disentangled trap qubit.
+'''Input''': <math>m</math> qubits sequentially.</br>
+'''Output''': entangled graph state with a disentangled trap qubit.
 * Server creates an entangled state from all received qubits using CZ operations according to their indices and creates the cylinder brickwork state.
@@ Line 100: / Line 100: @@
 '''Output''': <math>b_i</math>
-* For <math>i = 1, 2, ... m-n</math>:
+* For <math>i = 1, 2, ... m-n</math> (received qubits):
 ** Client computes <math>\phi_i</math>.
-*** if <math>i == t</math>:
+*** if <math>i == t</math>, then <math>\phi_i = 0</math>
-**** <math>\phi_i = 0</math>
+** Client randomly selects <math>r_i</math> and generates <math>\theta'_i = \theta_i + r_i</math>.
-** Client randomly selects <math>r_i</math>.
+** Client then computes the angle <math>\delta_i = \phi_i + \sum_{j:i \in N_g(f(j)}\theta'_i + s_i\pi</math> and sends <math>\delta_i</math> to server.
-** Client then computes the angle <math>\delta_i</math> and sends this to the server.
+** Server measures <math>i</math> and sends <math>b_i</math> to client.
-<div style="text-align: center;"><math>\delta_i = \phi^{'}_i + \theta_i + r_i\pi</math></div>
+** Client sets the value <math>s_i = b_i \oplus r_i</math> in <math>s</math>
-** Server measures <math>b_i</math> and sends it to client.
-** Client sets the value of <math>s_i</math> in <math>s</math> to be <math>b_i \oplus r_i</math>.
 '''Stage 4: '''Verification:</br>
 '''Input''': Output qubits <math>m-n+1</math> to <math>m</math></br>
 '''Output''': Verification result
-* For <math>i = m-n+1, ... m</math>:
+* For <math>i = m-n+1, ... m</math> (output qubits):
-** Server sends output qubit <math>i</math> to client.
+** Server sends <math>i</math> to client.
 * Client measures the output trap qubit <math>t</math> (which was disentangled) with angle <math>\delta_t = \phi_t + r_t\pi</math>.
 ** Client obtains the result <math>b_t</math>.
-*** If <math>b_t == r_t</math>:
+*** If <math>b_t == r_t</math>, then computation is accepted.
-**** Computation is accepted.
+*** else, computation is rejected.
-*** else:
-**** Computation is rejected.
 ==Further Information==
 <div style='text-align: right;'>''*contributed by Rhea Parekh''</div>