A quantum state is a mathematical representation of a physical system, such as an atom, and provides the basis for processing quantum information.

Outline:

a. Quantum states are represented by directions or vectors in an abstract space.

b. The direction of the quantum state vector expresses the probabilities of all of the possible outcomes of a set of measurements. Quantum manipulations in the physical world follow vector operations, incorporating complex numbers and negative values. This captures a behavior of physical quantum systems that cannot be described solely by the arithmetic of probability.

c. Quantum systems are fragile. For instance, measurement almost always disturbs a quantum system in a way that cannot be ignored. This fragility influences the design of computational algorithms and communication and sensing protocols.

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Prerequisite Knowledge:

-Directions or vectors

-Probability