Define quantum entanglement.

Quantum entanglement is a phenomenon in quantum mechanics.

It involves two or more quantum particles.

These particles become linked in such a way that their fates are correlated, irrespective of the distance separating them.

A measurement performed on one entangled particle instantaneously influences the state of the other entangled particle(s).

This correlation persists even when the particles are separated by vast distances.

It is a fundamentally non-classical phenomenon, defying classical intuition about locality and independent properties.

The combined state of entangled particles cannot be described by the states of the individual particles independently.

Entanglement is a resource for quantum information processing, including quantum computing and quantum communication.

Einstein famously referred to it as “spooky action at a distance.”

Bell’s theorem and subsequent experiments have confirmed the reality of entanglement and its non-local nature.

Quantum Mechanics: The fundamental theory describing the physical properties of nature at the scale of atoms and subatomic particles.

Superposition: A quantum principle where a particle can exist in multiple states simultaneously until a measurement is made.

Quantum State: A mathematical description of the state of a quantum system, typically represented by a wave function.

Correlation: A statistical relationship between two or more variables. In entanglement, these correlations are stronger than any possible in classical physics.

Non-locality: The property of entanglement where events at one location can instantaneously affect outcomes at another distant location, without any apparent physical connection or signal traveling between them.

Wave Function Collapse: The process by which a quantum system’s state transitions from a superposition of possibilities to a single definite outcome upon measurement.

Quantum Information: Information encoded in quantum systems, which can leverage phenomena like entanglement for enhanced processing and communication.

Bell Inequalities: Mathematical inequalities that set limits on correlations achievable in classical physics. Violations of these inequalities are strong evidence for quantum entanglement.

Quantum entanglement is one of the most profound and counter-intuitive phenomena predicted by quantum mechanics.

It describes a unique connection between quantum particles where their properties become intrinsically linked, regardless of the spatial separation between them.

This interconnectedness means that the state of one entangled particle cannot be described independently of the states of the other particles in the entangled set.

The measurement of a property on one particle instantaneously influences the corresponding property of its entangled partners, a correlation that has no equivalent in classical physics.

Quantum entanglement arises when two or more quantum particles interact in a specific way, leading to a shared quantum state.

Consider two particles, A and B, that become entangled. Their combined quantum state is not simply the sum of their individual states; rather, it is a single, unified state that describes both particles simultaneously.

A key characteristic is that if a property of particle A (e.g., its spin) is measured and found to be in a certain state (e.g., spin up), then the corresponding property of particle B will be instantaneously determined to be in a correlated state (e.g., spin down), even if B is light-years away.

This instantaneous correlation implies that information about the state of one particle is immediately available from the state of the other, a concept that challenges our classical understanding of locality, which posits that influences can only propagate at or below the speed of light.

Mathematically, an entangled state cannot be factored into a product of individual states for each particle. For instance, a simple non-entangled state of two qubits might be represented as |ψ_A⟩ ⊗ |ψ_B⟩, meaning qubit A is in state |ψ_A⟩ and qubit B is in state |ψ_B⟩, independently. However, an entangled state, such as the Bell state |Φ⁺⟩ = (1/√2)(|00⟩ + |11⟩), cannot be written in this separable form.

The strangeness of this phenomenon led Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR) to question the completeness of quantum mechanics, suggesting the existence of “hidden variables” that predetermine these outcomes. However, John Stewart Bell’s theorem provided a theoretical framework to experimentally test this idea.

Subsequent experiments, notably those by Alain Aspect and others, have repeatedly violated Bell’s inequalities, providing strong evidence that entanglement is a real phenomenon and that local hidden variable theories are incorrect. This experimental confirmation solidifies the non-local nature of quantum entanglement.

Entanglement is not just a theoretical curiosity; it is a crucial resource for emerging quantum technologies. It underpins quantum computing, enabling the parallel processing of information. It is also vital for quantum communication protocols like quantum teleportation and secure quantum cryptography, where the correlated nature of entangled particles can be used to transmit information with unparalleled security and efficiency.

In summary, quantum entanglement is a unique and profound quantum mechanical phenomenon where two or more particles become inextricably linked, sharing a single quantum state.

This linkage results in instantaneous correlations between their measured properties, irrespective of their spatial separation, a feature that defies classical notions of locality.

While initially a source of debate and disbelief, experimental evidence has firmly established entanglement as a fundamental aspect of reality.

Beyond its theoretical significance, quantum entanglement serves as a powerful resource driving advancements in quantum computing, secure communication, and other transformative quantum technologies.