Quantum entanglement is one of the most fascinating and counterintuitive aspects of quantum mechanics. It challenges our classical notions of locality and reality, suggesting that particles can be correlated in ways that defy common sense. This blog will take you through a deep understanding of quantum entanglement, including its mathematical formulation, real-world examples, and experimental evidence. If you have a basic understanding of quantum physics (such as wave functions and superposition), this blog will help you grasp entanglement with clarity.
1. What is Quantum Entanglement?
At its core, quantum entanglement describes a situation where two or more quantum systems become so deeply connected that their properties are no longer independent, no matter how far apart they are.
Let’s begin with a simple analogy:
Example: Two Coins in a Box
Imagine you have two coins inside two sealed boxes. You send one box to a friend on the other side of the world. Before opening the boxes, you don’t know whether a coin is heads or tails. However, when you open your box and see heads, you immediately know that your friend’s coin must be tails (assuming they were prepared as an opposite pair).
But this example is still classical. The real strangeness of quantum entanglement is that the state of each coin isn’t decided until you open the box. Before measurement, they exist in a superposition of heads and tails, and only when one is observed does the other instantly take the correlated value—no matter the distance between them.
2. Formulation of Entanglement
To understand entanglement mathematically, let’s consider a two-particle system.
In quantum mechanics, a system’s state is described by a wave function ψ (psi). For two particles, their combined wave function is:
$\Psi\rangle = c_1 |A\rangle \otimes |B\rangle + c_2 |C\rangle \otimes |D\rangle$
where:
- ∣A⟩,∣B⟩,∣C⟩,∣D⟩|A\rangle, |B\rangle, |C\rangle, |D\rangle are basis states of the particles.
- c1c_1 and c2c_2 are probability amplitudes.
A system is entangled when its wave function cannot be written as a product of individual wave functions of the two particles. That is, if: ∣Ψ⟩≠∣ψ1⟩⊗∣ψ2⟩|\Psi\rangle \neq |\psi_1\rangle \otimes |\psi_2\rangle
then the system is entangled.
Example: The Singlet State
A classic example of entanglement is the singlet state of two spin-½ particles (such as two electrons): ∣Ψ⟩=12(∣↑⟩1∣↓⟩2−∣↓⟩1∣↑⟩2)|\Psi\rangle = \frac{1}{\sqrt{2}} (|\uparrow\rangle_1 |\downarrow\rangle_2 – |\downarrow\rangle_1 |\uparrow\rangle_2)
Here, neither electron has a definite spin until one is measured. If we measure the first electron’s spin and find it to be up (↑\uparrow), the second electron must be down (↓\downarrow)—instantaneously, no matter how far apart they are.
3. Bell’s Theorem: Testing Entanglement
One of the most significant results in quantum mechanics is Bell’s theorem, which shows that quantum entanglement cannot be explained by classical physics.
Classical vs. Quantum Correlations
Imagine two people, Alice and Bob, each receiving one of two entangled electrons. They perform spin measurements along different directions. Classical physics suggests that hidden variables might determine the results in advance. But quantum mechanics predicts a stronger correlation, violating what is known as Bell’s inequality.
Bell derived an inequality for the expectation values of spin measurements: ∣E(a,b)−E(a,c)∣+∣E(b,c)∣≤2|E(a, b) – E(a, c)| + |E(b, c)| \leq 2
where E(a,b)E(a, b) represents the correlation between measurements at angles aa and bb.
Quantum mechanics predicts that entangled particles violate this inequality, proving that no local hidden variable theory can explain their behavior. Experiments, such as those conducted by Alain Aspect in the 1980s, confirmed these quantum correlations.
Real-World Example: Polarized Light
If you pass light through a polarizer at 45°, some photons will pass, and some won’t. If two entangled photons are created and sent to two different detectors, their polarization measurements remain correlated even if the detectors are miles apart.
4. Experimental Evidence of Entanglement
Several key experiments have confirmed entanglement:
- Aspect’s Experiment (1981-1982): First strong experimental test of Bell’s theorem.
- Zeilinger’s Quantum Teleportation (1997): Successfully teleported quantum states using entanglement.
- Chinese Micius Satellite (2017): Demonstrated entanglement over 1,200 km.
These experiments show that entanglement is real, non-local, and fundamental to quantum mechanics.
5. Applications of Entanglement
Entanglement is not just a theoretical concept—it has profound practical applications.
Quantum Cryptography (QKD – Quantum Key Distribution)
Entanglement enables unbreakable encryption. In the BB84 protocol, Alice and Bob share entangled photons. Any eavesdropper trying to intercept them collapses their wave function, revealing the intrusion.
Quantum Computing
Entanglement allows qubits to store and process information in ways classical bits cannot. In a quantum computer, entangled qubits can solve problems exponentially faster than classical computers (e.g., factoring large numbers via Shor’s algorithm).
Quantum Teleportation
Quantum teleportation allows the transfer of quantum states over long distances using entanglement. This is not “teleporting” objects but transmitting information in a fundamentally secure way.
6. Can Entanglement Be Used for Faster-Than-Light Communication?
No. While measurement of one entangled particle instantaneously determines the state of the other, no usable information is transmitted faster than light. The measurement results are still random and require a classical channel for communication.
Quantum entanglement is one of the most bizarre yet experimentally verified aspects of physics. It defies classical intuition, proving that the universe is interconnected in ways we are only beginning to understand. From quantum cryptography to teleportation, entanglement is shaping the future of technology.
Understanding entanglement not only deepens our knowledge of quantum mechanics but also challenges our fundamental concepts of reality and information. While we have confirmed its existence and usefulness, many mysteries remain, making it a key area of ongoing research.