Measurement-Only Universal Blind Quantum Computation: Difference between revisions

Measurement-Only Universal Blind Quantum Computation (edit)

Revision as of 06:55, 11 July 2019

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 *'''Output:''' Client: Final Outcome
 #Server’s preparation
-##Server creates a resource state Gmxnxo
+##Server creates a resource state <math>G_{\text{mxnxo}}</math>
-#Interaction and Computation For i= 1 →m, j= 1 →n, k= 1 →o
+#Interaction and Computation
+##For i= 1,2,...m, j= 1,2,...n, k= 1,2,...o
 ##[Protocol 1a]
-###Server directly sends the qubit <math>|\psi\rangle_{i,j,k}</math> to Client
+###Server sends <math>|\psi\rangle_{i,j,k}\rangle</math> to Client
-###Client measures his qubit in the measurement basis according to the measurement pattern
+###Client measures <math>|\psi\rangle_{i,j,k}\rangle</math> in the required measurement basis according to her measurement pattern
 ##[Protocol 1b]
-###Server creates Bell pair
+###Server creates [[Glossary#Bell States|Bell pair]] <math>\phi_{1,2}=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)</math>
-###Server sends one half (<math>|\phi_2\rangle</math>) of the Bell pair to Client
+###Server sends to Client (<math>|\phi_2\rangle</math>) and waits for Client's response
-###Client tells her response to Server if she received the sent qubit or not iv. If she didn’t, Server repeats the previous two processes, otherwise
+###Client checks if she received and tells the Server as Client.Response()
-###Client measures her share of entangled qubit (<math>|\phi_2\rangle</math>) in measurement basis {<math>|0\rangle</math> &plusmn; <math>e^{i\theta}|1\rangle</math>} determined by measurement pattern.   in case of Clifford gates while {<math>\pi/4</math>} in case of non-Clifford gates.
+###'''If Client.Response()=No''', Server repeats the previous two steps
-###Server uses gate teleportation to apply this unknown gate on the qubit of resource state as follows
+###'''Else''' Client measures (<math>|\phi_2\rangle</math>) in measurement basis {<math>|0\rangle \pm e^{i\theta}|1\rangle</math> determined by measurement pattern.
-####He entangles his share of Bell pair with the qubit of the resource state <math>|\psi\rangle_{i,j,k}</math> by performing CZ
+###'''Server's Computation: [[Glossary#Gate Teleportation]]'''
-####He measures the qubit in the register, <math>|\psi\rangle_{i,j,k}</math> in X basis ({<math>|+\rangle,|-\rangle</math>}) and communicates the outcome to the Client. This applies the required measurement on the qubit of the resource state with some correction depending on the outcome
+####He entangles <math>|\phi_2\rangle</math> with <math>|\psi\rangle_{i,j,k}</math> by performing [[Gossary#Quantum Gates|C-Z]]
-####Client records Server’s outcome and uses it when computing the final result or measurement angles for further qubits
+####He measures <math>|\psi\rangle_{i,j,k}</math> in X basis ({<math>|+\rangle,|-\rangle</math>})
+####Server's applies correction on the classical outcome using Gate Teleporation.
+###Server communicates the corrected outcome.
+####Client records Server’s outcome and uses it when computing the final result or measurement angles for further qubits.
 *Interaction and Computation steps are repeated until all the qubits of resource state are measured.
 <div style='text-align: right;'>''*contributed by Shraddha Singh''</div>