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Weak String Erasure: Difference between revisions
→Pseudo Code
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See [[Weak String Erasure#References|(WSE?)]] for precise definition. | See [[Weak String Erasure#References|(WSE?)]] for precise definition. | ||
== | ==Pseudocode== | ||
'''Inputs:''' n</br> | '''Inputs:''' n</br> | ||
'''Output:''' <math>X_1^n</math>, <math>\mathcal{I}</math>, <math>X_{\mathcal{I}}</math>. | '''Output:''' <math>X_1^n</math>, <math>\mathcal{I}</math>, <math>X_{\mathcal{I}}</math>. | ||
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## Bob chooses uniformly at random <math>\hat \Theta_i \in\{0,1\}</math>. | ## Bob chooses uniformly at random <math>\hat \Theta_i \in\{0,1\}</math>. | ||
## Bob measures the incoming qubit in the standard basis if <math>\hat \Theta_i=0</math> and in the Hadamard basis otherwise. He gets outcome <math>\hat X_i</math> | ## Bob measures the incoming qubit in the standard basis if <math>\hat \Theta_i=0</math> and in the Hadamard basis otherwise. He gets outcome <math>\hat X_i</math> | ||
#At this stage Alice has string <math>X_1^n</math> and <math>\Theta_1^n</math>, and Bob has strings <math>\hat X_1^n</math> and <math>\hat \Theta_1^n</math>. | |||
# Alice and Bob wait for time <math>\Delta t</math>. | # Alice and Bob wait for time <math>\Delta t</math>. | ||
# Alice sends <math>\Theta_1^n</math> to Bob. | # Alice sends <math>\Theta_1^n</math> to Bob. | ||
# Bob computes <math>\mathcal{I}:=\{i \in [n] : \Theta_i = \hat \Theta_i\}</math>. | # Bob computes <math>\mathcal{I}:=\{i \in [n] : \Theta_i = \hat \Theta_i\}</math>. | ||
# Bob erases all bits from <math>\hat X_1^n< | # Bob erases all bits from <math>\hat X_1^n<math> with index <math>i\notin \mathcal{I}</math>. Bob holds string <math>\hat X_{\mathcal{I}}</math>, and we should have <math> X_{\mathcal{I}} = \hat{X}_{\mathcal{I}} <\math> | ||
==Further Information== | ==Further Information== | ||