Quantum entanglement is a phenomenon in which two or more particles are linked in such a way that the state of one particle cannot be described independently of the other, even when they are separated by a large distance.

A Bell state is a particular type of entangled state of two qubits, where each qubit is in a superposition of two states. Bell states are often used in quantum information processing and quantum cryptography.

The Aspect experiment, conducted by Alain Aspect and his colleagues in 1982, provided strong experimental evidence for the violation of Bell's inequality, which is a mathematical inequality that cannot be satisfied by any local hidden variable theory. This result is widely regarded as a definitive confirmation of quantum entanglement.

The 'spooky action at a distance' paradox refers to the apparent instantaneous communication between entangled particles, regardless of the distance between them. This phenomenon seems to violate the principle of locality, which states that no information can travel faster than the speed of light.

In quantum entanglement, the process of measuring the state of one entangled particle is known as quantum collapse. This process causes the wave function of the entangled particles to collapse, meaning that the particles instantly assume definite states.

Spin is a commonly used physical property of particles to demonstrate quantum entanglement. Entangled particles can have their spins correlated in such a way that measuring the spin of one particle instantly determines the spin of the other, regardless of the distance between them.

The 'no-communication theorem' states that entangled particles cannot be used to transmit information faster than the speed of light. This theorem ensures that quantum entanglement does not violate the principle of causality.

Quantum entanglement has the potential to revolutionize cryptography by enabling the development of unbreakable encryption protocols. These protocols rely on the non-local nature of entanglement to ensure the security of communication.

Erwin Schrödinger is widely credited with proposing the concept of quantum entanglement in his 1935 paper titled 'The Present Situation in Quantum Mechanics.'

The EPR paradox, also known as the Einstein-Podolsky-Rosen paradox, is a thought experiment that highlights the non-local nature of quantum entanglement. It raises questions about the completeness of quantum theory and the role of locality in quantum mechanics.

Quantum state preparation refers to the process of creating a pair of entangled particles in a desired quantum state. This process is crucial for initializing quantum entanglement experiments and applications.

Photons are commonly used to demonstrate quantum entanglement in laboratory experiments due to their ease of manipulation and detection. Entangled photons can be generated using various techniques, such as spontaneous parametric down-conversion and four-wave mixing.

Entanglement entropy quantifies the degree of entanglement between two quantum systems. It provides a mathematical framework for characterizing and understanding the non-local correlations exhibited by entangled particles.

Quantum teleportation is a quantum information processing task that utilizes the non-local nature of quantum entanglement to transfer the quantum state of one particle to another, distant particle.

The Schmidt decomposition is a mathematical tool used to represent entangled quantum states in terms of a set of orthonormal vectors. It provides a convenient way to analyze and manipulate entangled states.