Source-linked AI summary
Blind quantum computation protocol in which Alice only makes measurements
Tomoyuki Morimae, Keisuke Fujii
TL;DR
The paper addresses how a client with limited quantum technology can delegate computation without revealing the input, output, or algorithm. It proposes blind protocols in which Alice performs measurements rather than generating quantum states, and proves blindness using no-signaling while Protocol 2 supports loss-tolerant universal computation. The approach also establishes blindness for Alice’s output and measurement angles under the protocol’s stated assumptions.
Problem
Existing blind quantum computation protocols require Alice to generate quantum states, while this paper seeks secure delegation with a simpler measurement-only device.
Method
The paper uses measurement-based protocols in which Alice measures states supplied through Bob’s resource and analyzes blindness with no-signaling and conditional-probability arguments.
Results
The protocols preserve blindness of Alice’s computational angles and output, while Protocol 2 implements universal computation deterministically up to Pauli byproducts.
Takeaways & Limitations
Blind quantum computation can be implemented with Alice performing measurements, including a protocol that tolerates channel loss and supports universal computation.
Takeaways & Limitations
The blindness analysis assumes the initial computation state is standard and that input preparation is included in the computational part.
Abstract
from arXiv · showhide
Blind quantum computation is a new secure quantum computing protocol which enables Alice who does not have sufficient quantum technology to delegate her quantum computation to Bob who has a fully-fledged quantum computer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experimental setups, such as optical systems, the measurement of a state is much easier than the generation of a single-qubit state. Therefore our protocols ease Alice's burden. Furthermore, the security of our protocol is based on the no-signaling principle, which is more fundamental than quantum physics. Finally, our protocols are device independent in the sense that Alice does not need to trust her measurement device in order to guarantee the security.
BLINDNESS OF PROTOCOL 1
Protocol 1 defines blindness as preserving Bob’s prior uncertainty about Alice’s computational angles and final output, even after Bob uses available classical information and measurements. Its proofs apply the no-signaling condition to show Bob cannot learn either secret.
- Definition of blindness: Blindness requires Bob’s conditional distributions for Alice’s computational angles and final output to equal their a priori distributions.The protocol assumes the initial state is standard and treats input preparation as part of the computation.
- Operational meaning: Bob’s certainty about Alice’s information does not change even when he performs POVMs on his system.This summarizes the operational meaning of the blindness conditions.
- Blindness of computational angles: No-signaling makes Bob’s measurement-result distribution independent of Alice’s measurement angles.The proof explicitly equates P(MB = mB|A = a, B = b) and P(MB = mB|A = a′, B = b).
- Blindness of computational angles: Bayes’ theorem then shows Bob cannot learn anything about Alice’s measurement angles from his measurement results.The posterior distribution remains equal across alternative angle values.
- Blindness of the output: Changing Alice’s input can change her output, but no-signaling keeps Bob’s measurement statistics independent of that output.The proof uses this independence to compare alternative output values.
- Blindness of the output: Bayes’ theorem likewise shows Bob cannot learn anything about Alice’s final output.The posterior distribution of the output remains equal for alternative output values.
CORRECTNESS OF PROTOCOL 2
Protocol 2 uses Bell-pair teleportation and Alice’s measurements to implement a universal measurement-based computation without requiring her to maintain a single-particle quantum memory. Repeating the unit-cell procedure three times makes the operations deterministic up to Pauli byproducts.
- Protocol procedure: Protocol 2 has Alice request retransmission when channel loss prevents her from receiving Bob’s Bell-pair particle.After successful receipt, Alice measures the particle and communicates the measurement angle and result through the protocol steps.
- Protocol procedure: Alice’s measurement and Bob’s subsequent measurement implement the unit-cell transformation on Bob’s state.The construction uses a controlled-Z gate, rotated states, and a measurement in the {|+⟩, |−⟩} basis.
- Implemented operations: The protocol uses S = Rπ/2 and T = R−π/4 as elementary rotations, with Pauli byproducts tracked separately.Different Pauli byproducts may be represented by the same symbol P for simplicity.
- Implemented operations: Repeating the procedure three times implements the unit cell deterministically up to Pauli byproducts.This repetition establishes deterministic operation of the cell used in the protocol.
- Universality: The unit cell implements a universal set including single-qubit operations and CZ and CNOT interactions.The listed operations include I, SH, STH, ST†H, H, and the two-qubit gates CZ and CNOT.
- Universality: Tiling the unit cell creates a universal two-dimensional graph state resembling the brickwork state.The construction uses the operation set implemented by the unit cell.
BLINDNESS OF PROTOCOL 2
Protocol 2’s blindness proof incorporates Alice’s channel-loss message into Bob’s available information. Using no-signaling and Bayes’ theorem, the proof shows that this information does not reveal Alice’s measurement angles or output.
- Blindness analysis: The blindness analysis models Bob’s knowledge using his POVM type, POVM result, and Alice’s channel-loss message.The variable T represents Alice’s message about whether the channel transmission succeeded.
- Blindness of measurement angles: Bayes’ theorem is applied to Alice’s measurement-angle distribution conditioned on Bob’s information and the loss message.The proof compares alternative angle values while retaining the same observed variables.
- Blindness of measurement angles: The resulting equality shows Bob cannot update his knowledge of Alice’s measurement angles from the protocol transcript and POVM results.The posterior for one angle value equals the posterior for an alternative value.
- Blindness of the output: Theorem 4 analyzes Alice’s output conditioned on Bob’s POVM type, POVM result, and channel-loss message.This extends the blindness analysis from measurement angles to the final output.
- Blindness of the output: The same proof structure is organized around conditional probabilities of the output given Bob’s observations.The supplied proof setup identifies the variables used to evaluate Bob’s knowledge.