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→Bell states or Two-qubit Maximally Entangled States
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<math>|\Phi^+\rangle = \frac{1}{sqrt{2}} (|00\rangle + |11\rangle)</math><br/> | <math>|\Phi^+\rangle = \frac{1}{sqrt{2}} (|00\rangle + |11\rangle)</math><br/> | ||
This is one of the Bell states. | This is one of the Bell states. | ||
===Bell | ===Bell States=== | ||
Bell states are maximally-entangled two-qubit states. These are the states that violate the Bell's inequality with maximal value of <math>2\sqrt{2}</math>. These states make a compelete basis for the two-qubit (4 dimensional) Hilbert space:<br/> | Bell states are maximally-entangled two-qubit states. These are the states that violate the Bell's inequality with maximal value of <math>2\sqrt{2}</math>. These states make a compelete basis for the two-qubit (4 dimensional) Hilbert space:<br/> | ||
<div style='text-align: center;'> | <div style='text-align: center;'> | ||
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<math>|\Psi ^{+}\rangle =\frac{1}{\sqrt{2}}(|0\rangle_{A}\otimes |1\rangle_{B}+|1\rangle_{A}\otimes |0\rangle_{B}) </math></br> | <math>|\Psi ^{+}\rangle =\frac{1}{\sqrt{2}}(|0\rangle_{A}\otimes |1\rangle_{B}+|1\rangle_{A}\otimes |0\rangle_{B}) </math></br> | ||
<math>|\Psi ^{-}\rangle =\frac{1}{\sqrt{2}}(|0\rangle_{A}\otimes |1\rangle_{B}-|1\rangle_{A}\otimes |0\rangle_{B}) </math><br/></div> | <math>|\Psi ^{-}\rangle =\frac{1}{\sqrt{2}}(|0\rangle_{A}\otimes |1\rangle_{B}-|1\rangle_{A}\otimes |0\rangle_{B}) </math><br/></div> | ||
===Bell State Measurement=== | |||
Bell state measurement is termed as the projection of two qubits into one of the four Bell States as described above. It is done operating a Hadamard gate on one qubit and then, operating a C-NOT gate with this qubit as control and the other qubit as target. | |||
Experimental implementation of BSM is shown in [https://arxiv.org/pdf/1304.1214.pdf] | |||
===Fidelity=== | ===Fidelity=== | ||
The Fidelity is a quantum distance measure between two quantum states. For two general state $\rho$ and $\sigma$ it is defined as followes:<br/><br/> | The Fidelity is a quantum distance measure between two quantum states. For two general state $\rho$ and $\sigma$ it is defined as followes:<br/><br/> | ||