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Quantum Fingerprinting: Difference between revisions
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* Given an <math>n</math>-bit input, the protocol requires a quantum fingerprint of minimum <math>\log{}n</math> bits which contains quantum information. | * Given an <math>n</math>-bit input, the protocol requires a quantum fingerprint of minimum <math>\log{}n</math> bits which contains quantum information. | ||
* The quantum fingerprint is defined as the state <math>|h_x\rangle</math>, where <math>{E(x)}</math> is the fingerprint of the input <math>x</math>. <math>{E_i(x)}</math> is the <math>{i^{th}}</math> bit of <math>{E(x)}</math>. </br> | * The quantum fingerprint is defined as the state <math>|h_x\rangle</math>, where <math>{E(x)}</math> is the fingerprint of the input <math>x</math>. <math>{E_i(x)}</math> is the <math>{i^{th}}</math> bit of <math>{E(x)}</math>. </br> | ||
<math>|h_x\rangle = \frac{1}{\sqrt{m}}\sum_{ | <math>|h_x\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(x)\rangle</math> | ||
* The hamming distance i.e. the number of positions between two strings of same length, at which the corresponding symbols are different, of <math>{E(x)}</math> and <math>{E(y)}</math> is at least <math>{(1+\delta)m}</math>. | * The hamming distance i.e. the number of positions between two strings of same length, at which the corresponding symbols are different, of <math>{E(x)}</math> and <math>{E(y)}</math> is at least <math>{(1+\delta)m}</math>. | ||
* Any two fingerprints, <math>|h_x\rangle</math> and <math>|h_y\rangle</math> have an inner product of at most <math>{\delta}</math>. | * Any two fingerprints, <math>|h_x\rangle</math> and <math>|h_y\rangle</math> have an inner product of at most <math>{\delta}</math>. | ||