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→Quantum SWAP test
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If <math>|\psi\langle|\psi'\rangle \leq \delta</math>, then the ancilla qubit, after performing a Hadamard Gate and upon measurement, passes the test with probability <math>\frac{1+\delta^2}{2}</math> | If <math>|\psi\langle|\psi'\rangle \leq \delta</math>, then the ancilla qubit, after performing a Hadamard Gate and upon measurement, passes the test with probability <math>\frac{1+\delta^2}{2}</math> | ||
and fails the test with probability <math>\frac{1-\delta^2}{2}</math>. Hence, the SWAP test always passes for the same inputs and sometimes fails if they are different. By repeating the SWAP test, its efficiency can be amplified. | and fails the test with probability <math>\frac{1-\delta^2}{2}</math>. Hence, the SWAP test always passes for the same inputs and sometimes fails if they are different. By repeating the SWAP test, its efficiency can be amplified. | ||
===Quantum Capable Homomorphic Encryption=== | |||
*'''Homomorphic Encryption'''<br/>A homomorphic encryption scheme HE is a scheme to carry out classical computation from the Server while hiding the inputs, outputs and computation. It can be divided into following four stages. | |||
* ''Key Generation.'' The algorithm (pk,evk,sk) ← HE.Keygen(1λ) takes a λ, a security parameter as input and outputs a public key encryption key pk, a public evaluation key evk and a secret decryption key sk. | |||
* ''Encryption.'' The algorithm c ← HE.Encpk(µ) takes the public key pk and a single bit message µ ∈ {0,1} and outputs a ciphertext c. The notation HE.Encpk(µ;r) is be used to represent the encryption of a bit µ using randomness r. | |||
* ''Decryption''. The algorithm µ∗ ← HE.Decsk(c) takes the secret key sk and a ciphertext c and outputs a message µ∗ ∈ {0,1}. | |||
* ''Homomorphic Evaluation'' The algorithm cf ← HE.Evalevk(f,c1,...,cl) takes the evaluation key evk, a function f : {0,1}l → {0,1} and a set of l ciphertexts c1,...,cl, and outputs a ciphertext cf. It must be the case that: | |||
HE.Decsk(cf) = f(HE.Decsk(c1),...,HE.Decsk(cl)) (1) | |||
with all but negligible probability in λ. This means classical HE decrypts ciphertext bit by bit. | |||
HE scheme is compact if HE.Eval is independent of any inputs or computation. It is fully homomorphic if it can compute any boolean computation. | |||
*'''Quantum Capable'''<br/> | |||
''A classical HE is quantum capable if it can be used to evaluate quantum circuits.'' | |||
Any HE scheme to be quantum capable requires the following two properties. | |||
*''invariance of ciphertext:'' | |||
*''natural XOR operation:'' | |||
==References== | ==References== | ||
<div style='text-align: right;'>''*contributed by Shraddha Singh''</div> | <div style='text-align: right;'>''*contributed by Shraddha Singh''</div> | ||