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Weak String Erasure: Difference between revisions
→Properties
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==Properties== | ==Properties== | ||
* If (dishonest) Bob holds a quantum memory of dimension at most <math>d</math>, then his (smooth) min-entropy is lower bounded as follows,</br> | * If (dishonest) Bob holds a quantum memory of dimension at most <math>d</math>, then his (smooth) min-entropy is lower bounded as follows,</br> | ||
<math>H_{\min}^\epsilon(X_1^n | K \Theta_1^n M) \geq n \gamma\left(\frac{-\ | <math>H_{\min}^\epsilon(X_1^n | K \Theta_1^n M) \geq n \gamma\left(\frac{-\log_2(d)}{n}\right) -1- \log_2\frac{2}{\epsilon^2},</math></br> | ||
where <math>K</math> is any classical information Bob can hold, and | where <math>K</math> is any classical information Bob can hold, and <math>M</math> represent Bob's quantum state in his memory. This quantum state has dimension at most <math>d</math>. | ||
* Alice is ignorant about the set <math>\mathcal{I}</math>, the set of rounds in which Alice and Bob have chosen the same basis. | * Alice is ignorant about the set <math>\mathcal{I}</math>, the set of rounds in which Alice and Bob have chosen the same basis. | ||