Electrons are in quantum superposition of different locations around the nuclei of atoms. Atoms do not have precisely localized positions either, but are rather in superpositions that spread around small regions of space. In principle, macroscopic systems, like apples, cats and human beings, are predicted to be in quantum superpositions of different locations too, although the effect is so small that it has not been observed in practice for macroscopic systems.

Quantum entangled particles exhibit strong correlations independently of how far apart they are. Entangled particles cannot be described individually, but rather as part of a joint system. This phenomenon is strongly connected to quantum non-local causality, which intrigued Einstein and his colleagues, Podolsky and Rosen, leading them to suggest in 1935 that quantum theory is incomplete. In 1965, John Bell developed a mathematical framework to analyse more rigorously the intuitions of Einstein, Podolsky and Rosen, in the now famously known Bell's theorem. Since then, many physicists around the world have deeply investigated this problem theoretically and experimentally, which has been recognized with the Nobel prize of physics in 2022 to Alain Aspect, John Clauser and Anton Zeilinger.

Quantum teleportation uses quantum entanglement to instantaneously communicate the quantum information encoded in quantum states, in principle between arbitrarily distant entangled particles. However, the quantum information is communicated with a fundamental error, which can only be corrected via the transmission of a classical message between the distant locations. This message must necessarily be communicated using a physical system (for example, radio waves, telephone, email, etc.), which cannot travel faster than the speed of light through a vacuum. Thus, quantum teleportation cannot be completed faster than the speed of light, respecting Einstein's theory of relativity.

Quantum cryptography allows the communication and manipulation of information with secrecy and security guaranteed by the laws of quantum physics. For example, in quantum key distribution, two distant parties, Alice and Bob, can establish a quantum communication link by the transmission of quantum systems, and use this link to establish a string of bits, called a key, known to them but secret to any third party. This key enables them to exchange messages that remain secret to any other parties via one-time pads.

A quantum computer is in principle able to perform very large number of computations in parallel on quantum systems that are in superposition of many different quantum states. Although building sufficiently powerful quantum computers is a very challenging technological problem, it is expected by many quantum physicists that quantum computers will revolutionize technology by solving very complex mathematical problems that are intractable by the most advanced classical supercomputers existing nowadays.

Although quantum mechanics has been developed over more than a century and it has overwhelming experimental evidence with many technological applications, there are big open problems in quantum physics. For example, quantum physicists do not completely understand what happens in a quantum measurement, and how quantum physics and gravity can be unified.