Question

What specific property of a Bell state ensures that the measurement of one qubit instantly determines the measurement outcome of the other?

Accepted Answer

The specific property of a Bell state that ensures the measurement outcome of one qubit determines the outcome of the other is quantum entanglement. A Bell state is a maximally entangled state of two qubits, meaning the system exists in a single, unified quantum state where the individual qubits do not possess independent physical properties. Mathematically, this is expressed as a superposition where the state of the two qubits is linked; for example, in the state known as the Phi-plus state, the qubits are always perfectly correlated such that they will both be measured as zero or both be measured as one. This correlation arises because the state is written as a sum of the individual qubit states rather than a product of them, which makes it impossible to describe the state of one qubit without referencing the state of the other. When you perform a measurement on one qubit, you collapse the wave function of the entire two-qubit system into a single definite state. Because the qubits were entangled, this collapse instantly forces the second qubit into the corresponding state defined by the initial Bell state relationship. This does not involve a physical signal traveling between the qubits; instead, it is a consequence of the two qubits sharing a single, non-local quantum identity that persists regardless of the distance between them.

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What specific property of a Bell state ensures that the measurement of one qubit instantly determines the measurement outcome of the other?