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In classical mechanics, the initial state of one or more bodies is measured; the state evolves according to the equations of motion; measurements of the final state are compared to predictions. In quantum mechanics, ensembles of identically prepared quantum states evolve according to the equations of motion and many repeated measurements are ...
In quantum mechanics a state space is a separable complex Hilbert space.The dimension of this Hilbert space depends on the system we choose to describe. [1] [2] The different states that could come out of any particular measurement form an orthonormal basis, so any state vector in the state space can be written as a linear combination of these basis vectors.
Quantum state tomography is a process by which, given a set of data representing the results of quantum measurements, a quantum state consistent with those measurement results is computed. [50] It is named by analogy with tomography, the reconstruction of three-dimensional images from slices taken through them, as in a CT scan.
Given a classical measure of the distinguishability of two probability distributions, one can motivate a measure of distinguishability of two quantum states as follows: if an experimenter is attempting to determine whether a quantum state is either of two possibilities or , the most general possible measurement they can make on the state is a ...
While standard quantum mechanics postulates wave function collapse to connect quantum to classical models, some extension theories propose physical processes that cause collapse. The in depth study of quantum decoherence has proposed that collapse is related to the interaction of a quantum system with its environment.
In quantum computing, classical shadow is a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. [1] Given an unknown state , a tomographically complete set of gates (e.g. Clifford gates), a set of observables {} and a quantum channel defined by randomly sampling from , applying it to and measuring the resulting state, predict the expectation ...
Holevo's theorem is an important limitative theorem in quantum computing, an interdisciplinary field of physics and computer science.It is sometimes called Holevo's bound, since it establishes an upper bound to the amount of information that can be known about a quantum state (accessible information).
Quantum decoherence is a mechanism through which quantum systems lose coherence, and thus become incapable of displaying many typically quantum effects: quantum superpositions become simply probabilistic mixtures, and quantum entanglement becomes simply classical correlations.