Write
33
edits
Prepare-and-Measure Certified Deletion: Difference between revisions
Prepare-and-Measure Certified Deletion (edit)
Revision as of 14:21, 4 February 2022
, 4 February 2022no edit summary
No edit summary |
No edit summary |
||
| Line 20: | Line 20: | ||
==Notation== | ==Notation== | ||
<!-- Connects the non-mathematical outline with further sections. --> | <!-- Connects the non-mathematical outline with further sections. --> | ||
* For any string <math>x \in \{0,1\}^n</math> and set <math>\mathcal{I} \subseteq [n], x|_\mathcal{I}</math> denotes the string <math>x</math> restricted to the bits indexed by <math>\mathcal{I}</math> | |||
* For <math>x,\theta \in \{0,1\}^n, |x^\theta\rangle = H^\theta|x\rangle = H^{\theta_1}|x_1\rangle \otimes H^{\theta_2}|x_2\rangle \otimes ... \otimes H^{\theta_n}|x_n\rangle</math> | |||
* <math>\mathcal{Q} := \mathbb{C}^2</math> denotes the state space of a single qubit,<math>\mathcal{Q}(n) := \mathcal{Q}^{\otimes n}</math> | |||
* <math>\mathcal{D(H)}</math> denotes the set of density operators on a Hilbert space <math>\mathcal{H}</math> | |||
* <math>\lambda</math>: Security parameter | |||
* <math>n</math>: Length, in bits, of the message | |||
* <math>m = \kappa(\lambda)</math>: Total number of qubits sent from encrypting party to decrypting party | |||
* <math>k</math>: Length, in bits, of the string used for verification of deletion | |||
* <math>s = m - k</math>: Length, in bits, of the string used for extracting randomness | |||
* <math>\tau = \tau(\lambda)</math>: Length, in bits, of error correction hash | |||
* <math>\mu = \mu(\lambda)</math>: Length, in bits, of error syndrome | |||
* <math>\theta</math>: Basis in which the encrypting party prepare her quantum state | |||
* <math>\delta</math>: Threshold error rate for the verification test | |||
* <math>\Theta</math>: Set of possible bases from which \theta is chosen | |||
* <math>\mathfrak{H}_{pa}</math>: Universal<math>_2</math> family of hash functions used in the privacy amplification scheme | |||
* <math>\mathfrak{H}_{ec}</math>: Universal<math>_2</math> family of hash functions used in the error correction scheme | |||
* <math>H_{pa}</math>: Hash function used in the privacy amplification scheme | |||
* <math>H_{ec}</math>: Hash function used in the error correction scheme | |||
* <math>synd</math>: Function that computes the error syndrome | |||
* <math>corr</math>: Function that computes the corrected string | |||
<!--==Knowledge Graph== --> | <!--==Knowledge Graph== --> | ||
<!-- Add this part if the protocol is already in the graph --> | <!-- Add this part if the protocol is already in the graph --> | ||