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

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

Revision as of 22:04, 10 October 2018

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→‎Protocol

Shraddha

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 **<math>\delta</math>, final measurement angle
-===Protocol===
+==='''Stage 1:''' Preparation====
-*Unless given specific mention in [.], following steps apply to all the three protocols 1a-1c
+*Input: Client: Dimensions of Brickwork State (m,n), Input States (ψ0,y) [Protocol 1b only], Auxilliary Input States (ψx,y)
-====Preparation Stage====
-*Input: Client: Dimeonsions of Brickwork State (m,n), Input States (ψ0,y) [Protocol 1b only], Auxilliary Input States (ψx,y)
 *Output: Server: Brickwork State Gmxn
- '''Client [Protocol 1a]'''
 # Client’s preparation
 ##For each column x = 1,...,n
 ###For each row y = 1,...,m
 #### Client prepares  and sends the qubits to Server.
- '''Client [Protocol 1b]'''
+  '''Server’s preparation'''
-# Client’s input preparation
+# Server creates an entangled state from all received qubits, according to their indices, by applying CTRL-Z gates between the qubits in order to create a brickwork state <math>G_{n×m}</math>.
-##For the input column (x = 0,y = 1,...,m) corresponding to Client’s input
-###	Client applies Z0,y(θ0,y) for θ0,y ∈R {0,π/4,2π/4,...,7π/4}.
-###	Client chooses i0,y ∈R {0,1} and applies . She sends the qubits to Server.
-#Client’s auxiliary preparation
-##For each column x = 1,...,n
-###For each row y = 1,...,m
-#### Client prepares |ψx,yi ∈R {|+θx,yi | θx,y = 0,π/4,2π/4,...,7π/4} and sends the qubits to Server.
- '''Client [Protocol 1c]'''
-# Client’s auxiliary preparation
-##For each column x = 1,...,n − 1
-###For each row y = 1,...,m
-#### Client prepares |ψx,yi ∈R {|+θx,yi | θx,y = 0,π/4,2π/4,...,7π/4} and sends the qubits to Server.
-#Client’s output preparation
-#### Client prepares the last column of qubits |ψn,yi = |+i (y = 1,...,m) and sends the qubits
-to Server.
-  '''Server’s preparation [Protocols 1a, 1b and 1c]'''
-# Server creates an entangled state from all received qubits, according to their indices, by applying ctrl-Z gates between the qubits in order to create a brickwork state Gn×m for Protocols 1a and 1c while Gn+1×m for Protocol 1b.
 ====Computation Stage====
 *Input: Client: Measurement Angle: δx,y
 *Output: Server: Measurement Outcome: sx,y
   '''Interaction and measurement'''
-#For each column x = 1,...,n [Protocols 1a and 1b]; For each column x = 1,...,n−1 [Protocol 1c]
+#For each column x = 1,...,n
 ##For each row y = 1,...,m
-###	For Protocols 1a and 1c, Client computes φ0x,y where{equation missing} <br/>For Protocol 1b, Client computes  with the special case .
+###Client computes φ0x,y where{equation missing} <br/>
 ###	Client chooses rx,y ∈R {0,1} and computes .
 ###	Client transmits δx,y to Server. Server measures in the basis {|+δx,yi,|−δx,yi}.
 ###	Server transmits the result sx,y ∈ {0,1} to Client.
 ###	If rx,y = 1 above, Client flips sx,y; otherwise she does nothing.
-  '''Output Correction [Protocol 1c only]'''
+  '''Output Correction [only for quantum outputs]'''
 #	Server sends to Client all qubits in the last layer.
 #	Client performs the final Pauli corrections .