How does measuring a qubit affect its state?
Measuring a qubit has a profound impact on its state in the field of Quantum Information. To understand this, we need to consider the principles of quantum mechanics and the concept of superposition. A qubit, which is the basic unit of quantum information, can exist in a superposition of two states, often represented as |0⟩ and |1⟩. These states are analogous to classical bits 0 and 1, but unlike classical bits, qubits can exist in a linear combination of both states simultaneously.
When we measure a qubit, we extract information about its state. However, the act of measurement causes the qubit to collapse into one of the two basis states (|0⟩ or |1⟩) with a certain probability. The probability of obtaining each outcome is determined by the amplitudes associated with the qubit's superposition.
To understand this better, let's consider an example. Suppose we have a qubit in the state |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex numbers representing the amplitudes of the respective states. The probability of measuring the qubit in the state |0⟩ is given by |α|^2, and the probability of measuring it in the state |1⟩ is |β|^2. Importantly, these probabilities must add up to 1.
Upon measurement, the qubit collapses into one of the basis states, and its state is no longer a superposition. If we measure the qubit and obtain the outcome |0⟩, the qubit will be in the state |0⟩ with certainty. Similarly, if we measure and obtain the outcome |1⟩, the qubit will be in the state |1⟩ with certainty. This collapse is often referred to as the "collapse of the wavefunction."
It is important to note that the act of measurement is irreversible and disturbs the qubit's state. Once the qubit has collapsed, any subsequent measurement of the same qubit will yield the same outcome. This property of measurement plays a important role in quantum computing algorithms, as it allows for the extraction of classical information from a quantum system.
Measuring a qubit affects its state by collapsing it into one of the basis states, destroying the superposition it was in. The outcome of the measurement is probabilistic, with the probabilities determined by the amplitudes associated with the qubit's superposition. Once measured, the qubit remains in the state corresponding to the measurement outcome.
Other recent questions and answers regarding EITC/QI/QIF Quantum Information Fundamentals:
- Is the quantum Fourier transform exponentially faster than a classical transform, and is this why it can make difficult problems solvable by a quantum computer?
- What it means for mixed state qubits going below the Bloch sphere surface?
- What was the history of the double slit experment and how it relates to wave mechanics and quantum mechanics development?
- Are amplitudes of quantum states always real numbers?
- How the quantum negation gate (quantum NOT or Pauli-X gate) operates?
- Why is the Hadamard gate self-reversible?
- If you measure the 1st qubit of the Bell state in a certain basis and then measure the 2nd qubit in a basis rotated by a certain angle theta, the probability that you will obtain projection to the corresponding vector is equal to the square of sine of theta?
- How many bits of classical information would be required to describe the state of an arbitrary qubit superposition?
- How many dimensions has a space of 3 qubits?
- Will the measurement of a qubit destroy its quantum superposition?
View more questions and answers in EITC/QI/QIF Quantum Information Fundamentals