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Alice then sends the first qubit through a Hadamard gate. Alice measures her qubits, obtaining one of four results, and sends this information to Bob. Given Alice's measurements, Bob performs one of four operations on his half of the EPR pair and recovers the original quantum state. [1] The following quantum circuit describes teleportation:
For example, if she measures a | , Bob must measure the same, as | is the only state where Alice's qubit is a | . In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value "0" or "1"—a most ...
Once Alice obtains her qubit in the entangled state, she applies a certain quantum gate to her qubit depending on which two-bit message (00, 01, 10 or 11) she wants to send to Bob. Her entangled qubit is then sent to Bob who, after applying the appropriate quantum gate and making a measurement , can retrieve the classical two-bit message.
Upon receiving the bit from Charlie, Alice will measure her qubit in the basis {| , | } or in the basis {| + , | }, conditionally on whether = or =, respectively. She will then label the two possible outputs resulting from each measurement choice as a = 0 {\displaystyle a=0} if the first state in the measurement basis is observed, and a = 1 ...
Bell states possess the property that measurement outcomes on the two qubits are correlated. As can be seen from the expression above, the two possible measurement outcomes are zero and one, both with probability of 50%. As a result, a measurement of the second qubit always gives the same result as the measurement of the first qubit.
A qubit is a two-level system, and when we measure one qubit, we can have either 1 or 0 as a result. One corresponds to odd parity, and zero corresponds to even parity. This is what a parity check is. This idea can be generalized beyond single qubits. This can be generalized beyond a single qubit and it is useful in QEC.
Unlike classical digital states (which are discrete), a qubit is continuous-valued, describable by a direction on the Bloch sphere. Despite being continuously valued in this way, a qubit is the smallest possible unit of quantum information, and despite the qubit state being continuous-valued, it is impossible to measure the value precisely ...
Her measurements, however, risk disturbing a particular qubit with probability 1 / 2 if she guesses the wrong basis. Bob proceeds to generate a string of random bits b ′ {\displaystyle b'} of the same length as b {\displaystyle b} and then measures the qubits he has received from Alice, obtaining a bit string a ′ {\displaystyle a'} .