How does the measurement of one entangled qubit affect the state of the other qubit, regardless of the distance between them? Provide an example to illustrate this.
In the field of Quantum Information, specifically Quantum Entanglement, the measurement of one entangled qubit has a profound effect on the state of the other qubit, regardless of the distance between them. This phenomenon, known as quantum entanglement, is one of the most intriguing and counterintuitive aspects of quantum mechanics.
To understand how the measurement of one entangled qubit affects the other, let's first consider the concept of entanglement itself. Entanglement occurs when two or more qubits become correlated in such a way that the state of one qubit cannot be described independently of the other qubits' states. This correlation persists even when the qubits are separated by vast distances.
When two qubits are entangled, their states are described by a joint quantum state that cannot be decomposed into individual states for each qubit. This joint state is often referred to as a superposition of all possible combinations of states for the qubits involved. The key feature of this joint state is that it is highly entangled, meaning that any measurement on one qubit instantaneously affects the state of the other qubit, regardless of the spatial separation between them.
To illustrate this, let's consider an example involving two entangled qubits, qubit A and qubit B. Suppose we prepare these qubits in an entangled state known as the Bell state, denoted as |Φ⁺⟩ = (|00⟩ + |11⟩)/√2. In this state, both qubits are in a superposition of being in the state |0⟩ or |1⟩, and they are correlated in such a way that if we measure qubit A and find it in the state |0⟩, then qubit B will also be in the state |0⟩, and vice versa.
Now, let's say we perform a measurement on qubit A and find it in the state |0⟩. As a result of this measurement, the state of qubit B instantaneously collapses into the state |0⟩ as well. This collapse is not due to any classical communication between the qubits but is a consequence of the entanglement between them. Similarly, if we were to measure qubit A and find it in the state |1⟩, qubit B would instantaneously collapse into the state |1⟩.
It is important to note that this instantaneous collapse of the state of qubit B occurs regardless of the spatial separation between the qubits. This feature of entanglement, often referred to as "spooky action at a distance," was famously described by Albert Einstein as "spukhafte Fernwirkung."
The measurement of one entangled qubit affects the other qubit because the act of measurement disturbs the delicate quantum state of the entangled system. This disturbance propagates instantaneously to the other qubit due to their entanglement, causing its state to collapse accordingly. This phenomenon is not limited by any distance and has been experimentally observed in various setups, including those involving entangled photons and trapped ions.
The measurement of one entangled qubit has a profound effect on the state of the other qubit, regardless of the distance between them. This effect is a consequence of the entanglement between the qubits, where their states are correlated in such a way that any measurement on one qubit instantaneously affects the state of the other qubit. This phenomenon, known as quantum entanglement, is a fundamental aspect of quantum mechanics and has been experimentally verified in numerous experiments.
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