Entangled Qubits, Precise Meaning.
The precise meaning of entangled qubits can be understood through several key concepts:
**1. Quantum Superposition:**
* **Single Qubit:** Unlike a classical bit that can be either 0 or 1, a qubit can exist in a superposition, meaning it can be a combination of both states 0 and 1 simultaneously. Mathematically, this is represented as: `|ψ> = α|0> + β|1>`, where α and β are complex numbers such that `|α|^2 + |β|^2 = 1`. `|α|^2` represents the probability of measuring the qubit in the state `|0>`, and `|β|^2` represents the probability of measuring it in the state `|1>`.
**2. Quantum Entanglement:**
* **Multiple Qubits:** Entanglement is a special correlation that arises when two or more qubits are linked together in such a way that their fates are intertwined, regardless of the physical distance separating them.
* **Joint State:** The state of entangled qubits cannot be described as a simple product of the individual qubit states. Instead, they are described by a **joint state**. For example, consider two qubits, A and B. A simple (non-entangled) state might be `|ψ> = (|0>_A + |1>_A)⊗(|0>_B + |1>_B)`, which simplifies to `|00> + |01> + |10> + |11>`. However, an entangled state might be `|ψ> = (|00> + |11>)/√2`.
* **Correlation Upon Measurement:** The key characteristic of entanglement is that when you measure the state of one entangled qubit, you instantly know something about the state of the other entangled qubit, no matter how far apart they are. The possible outcomes are correlated.
* In the example `|ψ> = (|00> + |11>)/√2`, if you measure qubit A and find it to be in the state `|0>`, you instantly know that qubit B is also in the state `|0>`. Similarly, if you measure qubit A and find it to be in the state `|1>`, you instantly know that qubit B is also in the state `|1>`.
* **Non-Classical Correlation:** This correlation is stronger than any correlation possible in classical physics. Classical correlations are based on pre-existing shared information. Entanglement, however, creates correlations that cannot be explained by pre-existing local variables. This violation of local realism is what makes entanglement so fundamentally quantum.
**3. Mathematical Description:**
* The state of entangled qubits is described by a **non-separable** joint state. A separable state is one that can be written as a tensor product of individual qubit states. An entangled state cannot be written in this form.
* **Example Bell State:** A common example of an entangled state is the Bell state: `|Φ+> = (|00> + |11>)/√2`. This is one of four Bell states, which are maximally entangled states of two qubits. The other Bell states are:
* `|Φ-> = (|00> - |11>)/√2`
* `|Ψ+> = (|01> + |10>)/√2`
* `|Ψ-> = (|01> - |10>)/√2`
**4. Important Implications and Limitations:**
* **No Faster-Than-Light Communication:** Although measurement on one qubit instantaneously influences the outcome of measuring the other entangled qubit, this *cannot* be used to transmit information faster than light. The outcome of a single measurement on one qubit is random. You can only observe the correlations between the two qubits by performing many measurements on identically prepared pairs. Therefore, you cannot control the state of the distant qubit to send a specific message.
* **Quantum Computing:** Entanglement is a crucial resource for quantum computing. It allows for the creation of complex quantum algorithms that can solve certain problems much faster than classical algorithms.
* **Quantum Cryptography:** Entanglement is used in quantum key distribution (QKD) protocols to create secure communication channels.
* **Fragility:** Entanglement is a delicate phenomenon. It can be easily destroyed by interactions with the environment (a process called decoherence). Maintaining entanglement is one of the major challenges in building quantum computers.
**In summary:**
Entangled qubits are qubits that are linked together in a non-classical way, described by a joint quantum state that cannot be separated into individual qubit states. Measuring the state of one entangled qubit instantaneously influences the possible outcomes of measuring the other, regardless of distance. This correlation is stronger than any classical correlation and is a key resource for quantum technologies like quantum computing and quantum cryptography. However, entanglement is fragile and susceptible to decoherence.
