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Pseudo-Secret Random Qubit Generator (PSQRG): Difference between revisions
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The [https://arxiv.org/abs/1802.08759 example protocol] enables fully-classical parties to generate secret single qubit states using only public classical channels and a single quantum Server. This functionality could be used to replace a quantum channel completely such that a classical Client can perform various quantum applications over classical network connected to a quantum Server. An application of this functionality could be to carry out [[Secure Client- Server Delegated Computation|Delegated Quantum Computation]] by just classical online communication and no quantum communication. It allows a fully classical Client to hide her data such that she instructs Server to generate random single qubit states hiding her inputs, outputs, circuit and perform quantum computation on it via [[Prepare-and-Send Universal Blind Quantum Computation|UBQC]] or [[Prepare-and-Send Verifiable Universal Blind Quantum Computation|VUBQC]]. It can also find use cases in other protocols like Quantum Money, Quantum Digital Signatures etc.. which need user to share his/her private quantum key over a quantum channel. | |||
==Use Case== | ==Use Case== | ||
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*Generating random qubits for protocols like quantum-key-distribution, quantum money, quantum coin-flipping, quantum signatures, two-party quantum computation, multiparty quantum computation etc. | *Generating random qubits for protocols like quantum-key-distribution, quantum money, quantum coin-flipping, quantum signatures, two-party quantum computation, multiparty quantum computation etc. | ||
'''Tags:''' [[Category: Two Party Protocols]] [[:Category: Two Party Protocols|Two Party]], [[Category: Universal Task]][[:Category: Universal Task|Universal Task]], [[Category: Quantum Functionality]] [[:Category: Quantum Functionality|Quantum Functionality]], Classical Online Communication, [[Superposition]], [[Supplementary Information#Collision Resistant Functions|Collision Resistant Functions]], [[Supplementary Information#Learning With Errors|Learning With Errors]] | |||
== Outline == | == Outline == | ||
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*'''Preimages Superposition.''' Server prepares two quantum registers (system comprising multiple qubits), first being control (containing inputs) and second being target (containing output of the function). Client instructs Server to create a superposition of input states by applying [[Hadamard|Hadamard gate]] (quantum fourier transform) on control register. She then instructs Server to apply a [[unitary gate|unitary gate]] (all quantum gates are represented by unitary matrices) which computes output of the function in the target register, taking input from the control register, thus yielding an entangled state from the Server's superposition state. Server is required to measure the target register in the computational basis (along Z axis) and get an outcome. This action would reduce the control register into a superposition of two pre-images corresponding to the measurement outcome of the target register. He conveys this outcome to the Client who computes, classically, the two pre-images using her trapdoor. This pair of pre-image would have some isolated similar qubits (without superposition) and a superposition of dissimilar qubits. The dissimilar qubits can be written as a superposition of isolated 0s and isolated 1s (a GHZ state), with [[X(NOT)|X (NOT) gates]] applied to qubits depending on the state of qubit in both the pre-images. If the last qubit belongs to the set of similar qubits, then Client aborts and this Stage is repeated. | *'''Preimages Superposition.''' Server prepares two quantum registers (system comprising multiple qubits), first being control (containing inputs) and second being target (containing output of the function). Client instructs Server to create a superposition of input states by applying [[Hadamard|Hadamard gate]] (quantum fourier transform) on control register. She then instructs Server to apply a [[unitary gate|unitary gate]] (all quantum gates are represented by unitary matrices) which computes output of the function in the target register, taking input from the control register, thus yielding an entangled state from the Server's superposition state. Server is required to measure the target register in the computational basis (along Z axis) and get an outcome. This action would reduce the control register into a superposition of two pre-images corresponding to the measurement outcome of the target register. He conveys this outcome to the Client who computes, classically, the two pre-images using her trapdoor. This pair of pre-image would have some isolated similar qubits (without superposition) and a superposition of dissimilar qubits. The dissimilar qubits can be written as a superposition of isolated 0s and isolated 1s (a GHZ state), with [[X(NOT)|X (NOT) gates]] applied to qubits depending on the state of qubit in both the pre-images. If the last qubit belongs to the set of similar qubits, then Client aborts and this Stage is repeated. | ||
*'''Squeezing.''' Client instructs Server to measure all the qubits of the control register in some basis chosen randomly by the Client, except the last one, and return to her the outcomes. The last unmeasured state contains the randomly prepared qubit hidden from the Server. Client can then compute the value of r by an equation (see Pseudo Code). This equation depends only on Client’s measurement basis angles, Server’s measurement outcome and the location of random X’s (unknown to the Server). Thus, the Client knows the state of her secret qubit prepared by the Server. | *'''Squeezing.''' Client instructs Server to measure all the qubits of the control register in some basis chosen randomly by the Client, except the last one, and return to her the outcomes. The last unmeasured state contains the randomly prepared qubit hidden from the Server. Client can then compute the value of r by an equation (see Pseudo Code). This equation depends only on Client’s measurement basis angles, Server’s measurement outcome and the location of random X’s (unknown to the Server). Thus, the Client knows the state of her secret qubit prepared by the Server. | ||
==Notations== | |||
== | |||
**<math>f_k</math>, function for target register | **<math>f_k</math>, function for target register | ||
**<math>t_k</math>, trapdoor for function <math>f_k</math> | **<math>t_k</math>, trapdoor for function <math>f_k</math> | ||
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**<math>b_i</math>, Server’s measurement outcome for qubit i in the control register | **<math>b_i</math>, Server’s measurement outcome for qubit i in the control register | ||
**<math>\theta</math>, classical description of the hidden input state | **<math>\theta</math>, classical description of the hidden input state | ||
==Pseudocode== | |||
==='''Stage1''' Preimages superposition=== | ==='''Stage1''' Preimages superposition=== | ||
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*''Trapdoor Function'' A family of functions <math>\{f_k : D \rightarrow R\}_{k\epsilon \{0,1\}}</math> is a trapdoor function if there exists a QPT algorithm Gen which on input <math>1^n</math> outputs <math>(k,t_k)</math>, where k represents the index of a function, <math>\{f_k : D \rightarrow R\}_{k\epsilon \{0,1\}}</math>, where <math>f_k</math> is a one-way function, then there exists a QPT algorithm Inv, which on inputs <math>t_k</math> (which is called the trapdoor information) which was output by Gen(<math>1^n</math>), and <math>y = f_k(x)</math> can invert y (by returning all pre-images of y with non-negligible probability over the choice of <math>(k,t_k)</math> and uniform choice of x. | *''Trapdoor Function'' A family of functions <math>\{f_k : D \rightarrow R\}_{k\epsilon \{0,1\}}</math> is a trapdoor function if there exists a QPT algorithm Gen which on input <math>1^n</math> outputs <math>(k,t_k)</math>, where k represents the index of a function, <math>\{f_k : D \rightarrow R\}_{k\epsilon \{0,1\}}</math>, where <math>f_k</math> is a one-way function, then there exists a QPT algorithm Inv, which on inputs <math>t_k</math> (which is called the trapdoor information) which was output by Gen(<math>1^n</math>), and <math>y = f_k(x)</math> can invert y (by returning all pre-images of y with non-negligible probability over the choice of <math>(k,t_k)</math> and uniform choice of x. | ||
<div style='text-align: right;'>''*contributed by Shraddha Singh''</div> | <div style='text-align: right;'>''*contributed by Shraddha Singh''</div> | ||