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Quantum physics is moving out of the laboratory and into everyday life. Despite headline results about quantum computers solving problems impossible for classical computers, technical challenges are standing in the way of ...

Precise measurements find a crack in universal physics

The concept of universal physics is intriguing, as it enables researchers to relate physical phenomena in a variety of systems, irrespective of their varying characteristics and complexities. Ultracold atomic systems are ...

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A device that can separate and recombine pairs of electrons may offer a way to study an unusual form of superconductivity, according to RIKEN physicists. This superconducting state would involve exotic particles called Majorana ...

Ultrafast stimulated emission microscopy of single nanocrystals

The ability to investigate the dynamics of single particle at the nano-scale and femtosecond level remained an unfathomed dream for years. It was not until the dawn of the 21st century that nanotechnology and femtoscience ...

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Quantum state

In quantum physics, a quantum state is a mathematical object that fully describes a quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus. Quantum states can be statistically mixed, corresponding to an experiment involving a random change of the parameters. States obtained in this way are called mixed states, as opposed to pure states, which cannot be described as a mixture of others. When performing a certain measurement on a quantum state, the result generally described by a probability distribution, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. However, unlike in classical mechanics, the result of a measurement on even a pure quantum state is only determined probabilistically. This reflects a core difference between classical and quantum physics.

Mathematically, a pure quantum state is typically represented by a vector in a Hilbert space. In physics, bra-ket notation is often used to denote such vectors. Linear combinations (superpositions) of vectors can describe interference phenomena. Mixed quantum states are described by density matrices.

In a more general mathematical context, quantum states can be understood as positive normalized linear functionals on a C* algebra; see GNS construction.

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