the state of a single qubit, and coherence is lost. The result of the measurement of a single qubit with the state will be either with probability or with probability . Measurement of the state of the qubit alters the magnitudes of α and β. For instance, if the result of the measurement is , α is changed to 0 and β is changed to the phase factor no longer experimentally accessible. If measurement is performed on a qubit that is entangled, the measurement may collapse the state of the other entangled qubits. Initialization or re-initialization to a known value, often . This operation collapses the quantum state (exactly like with measurement). Initialization to may be implemented logically or physically: Logically as a measurement, followed by the application of the Pauli-X gate if the result from the measurement was . Physically, for example if it is a superconducting phase qubit, by lowering the energy of the quantum system to its ground state. Sending the qubit through a quantum channel to a remote system or machine (an I/O operation), potentially as part of a quantum network. Quantum entanglement An important distinguishing feature between qubits and classical bits is that multiple qubits can exhibit quantum entanglement. Quantum entanglement is a nonlocal property of two or more qubits that allows a set of qubits to express higher correlation than is possible in classical systems. The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the Bell state: In this state, called an equal superposition, there are equal probabilities of measuring either product state or , as . In other words, there is no way to tell if the first qubit has value “0” or “1” and likewise for the second qubit. Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either or , i.e., she can now tell if her qubit has value “0” or “1”. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. 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