Editing Trap Code for Quantum Authentication
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==Notation== | ==Notation== | ||
*<math>\rho</math>: 1-qubit input state | *<math>\rho</math>: 1-qubit input state | ||
==Protocol Description== | ==Protocol Description== | ||
*'''''Encoding:''''' | *'''''Encoding:''''' | ||
#<math>\ | #Input: <math>\rho</math>, pair of keys <math>k=(k_1, k_2)</math> | ||
#Apply an <math>[[n,1,d]]</math> error correction code (corrects up to <math>t</math> errors, <math>d=2t+1</math>) | |||
# | #Append an additional trap register of <math>n</math> qubits in state <math>|0\rangle\langle 0|^{\otimes n}</math> | ||
# | #Append a second additional trap register of <math>n</math> qubits in state <math>|+\rangle\langle +|^{\otimes n}</math> | ||
# | #Permute the total <math>3n</math>-qubit register by <math>\pi_{k_1}</math> according to the key <math>k_1</math> | ||
#Apply a Pauli encryption <math>P_{k_2}</math> according to key <math>k_2</math> | |||
*'''''Decoding:''''' | *'''''Decoding:''''' | ||
#<math>\ | #Input: <math>\rho^\prime</math> (state after encoding), pair of keys <math>k=(k_1, k_2)</math> | ||
# | #Apply <math>P_{k_2}</math> according to key <math>k_2</math> | ||
# | #Apply inverse permutation <math>\pi_{k_1}^\dagger</math> according to the key <math>k_1</math> | ||
# | #Measure the last <math>n</math> qubits in the Hadamard basis | ||
#Measure the second last <math>n</math> qubits in the computational basis </br>a. If the two measurements result in <math>|+\rangle\langle +|</math> and <math>|0\rangle\langle 0|</math>, an additional flag qubit in state <math>|\mathrm{ACC}\rangle\langle\mathrm{ACC}|</math> is appended and the quantum message is decoded according to the error correction code </br>b. Otherwise, an additional flag qubit in state <math>|\mathrm{REJ}\rangle\langle\mathrm{REJ}|</math> is appended and the (disturbed) encoded quantum message is replaced by a fixed state <math>\Omega</math> | |||
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#[https://arxiv.org/pdf/1211.1080.pdf| Broadbent et al. (2012)] | #[https://arxiv.org/pdf/1211.1080.pdf| Broadbent et al. (2012)] | ||
#[https://arxiv.org/pdf/1607.03075.pdf| Broadbent and Wainewright (2016).] | #[https://arxiv.org/pdf/1607.03075.pdf| Broadbent and Wainewright (2016).] | ||
<div style='text-align: right;'>''contributed by Shraddha Singh and Isabel Nha Minh Le''</div> | |||
<div style='text-align: right;'>'' | |||