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What is Quantum Entanglement?
When two or more quantum particles get entangled, their states are directly related to each other’s states regardless of the distance between them. These interesting and basic phenomena is known as quantum entanglement and it occurs in quantum mechanics. Quantum computing, encryption, and communication can all benefit greatly from this non-classical relationship.
Mathematical Representation
For two qubits, the system can be entangled into a state like:
∣ψ⟩=1/√2 (|00⟩+ |11⟩)
- ∣00⟩Both particles are in state 0.
- ∣11⟩: Both particles are in state 1.
- The superposition means the two particles are correlated, even if physically separated.
Properties
Non-locality: The state of one particle can be instantly derived from the state of another, independent of their distance from each other. Since light is the speed at which information travels, this does not go against the laws of relativity.
Inseparability: Entangled states cannot be expressed as a product of individual states.
Example: ∣ψ⟩=1/√2 (|00⟩+ |11⟩) is not separable as ∣ψ1⟩⊗∣ψ2⟩.
Entangled States:
Bell states: It is an entangled state of two-state particles, like
1√2 (|00⟩+ |11⟩) or 1√2 (|01⟩+ |10⟩)
Teleportation and superdense coding are two quantum techniques that are based on Bell states, which are maximally entangled two-qubit states.
GHZ states: In GHZ states, three or more particles are entangled. The actual realization of GHZ states, first in a single molecule using nuclear magnetic resonance and then with photons that are spread out in space, is seen as a major step forward in the processing of quantum information.
Characteristics of Entangled States:
Each particle in an entangled set has a quantum state that can’t be explained without mentioning the other particles, even if they are physically separated. Because they are connected, any action or test done on one entangled particle changes the state of the other entangled particles right away, no matter how far apart they are.
Entanglement occurs spontaneously as a result of interactions between quantum systems, such as the simultaneous formation of particles with conserved properties like spin or polarization. Measuring one particle’s spin immediately discloses the spin of the other if two particles are produced so that their total spin is zero as they must be opposing to preserve the zero total spin.
Simple product of individual qubit states cannot adequately represent an entangled state of several qubits. This implies that the composite state solely arises from their connectivity and has characteristics not attributable to any one qubit in isolation.
How Quantum Entanglement Works
Preparation of Entanglement: Entanglement is created through collisions of particles or controlled quantum operations like the CNOT gate in quantum circuits.
Measurement:Measurement: If you measure one qubit, it immediately affects the other qubit, collapsing their shared state.
Ex: Measure Qubit A from 1/√2 (|00⟩+ |11⟩) and find ∣0⟩
Qubit B’s state instantly collapses to ∣0⟩
Correlation: Depending on the entangled state, the results of measurements show perfect correlation (or anti-correlation).
Applications of Quantum Entanglement
Quantum Computing:
Entanglement is important for algorithms like Shor’s and Grover’s, providing computational advantages and also enabling the implementation of quantum gates like the Bell state generator.
Quantum Communication:
- Quantum Teleportation: Using entanglement to transfer quantum information (qubit states) between distant locations without physically transmitting the qubit itself.
- Quantum Key Distribution (QKD): Provides secure communication channels (e.g., BB84 protocol).
Quantum Cryptography
Entanglement ensures that any snooping on communication disrupts the system, revealing the intrusion.
Simulation of Quantum Systems
Entanglement enables efficient simulation of quantum systems that are otherwise intractable for classical computers.
Challenges and Limitations.
1. Decoherence: Environmental interactions can disrupt the correlation between entangled states.
2. Maintaining entanglement across long distances needs powerful quantum error correction techniques.
3. Scalability: Research is continuing to generate and manage large-scale entangled states for practical applications.