Statement
A bipartite state transforms to another using local operations and classical communication if and only if is majorized by where the are the Schmidt coefficients of the respective state.
This can be written more concisely as
iff .
Nielsen's theorem is a result in quantum information concerning transformations between bipartite states due to Michael Nielsen. [1] It makes use of majorization.
A bipartite state transforms to another using local operations and classical communication if and only if is majorized by where the are the Schmidt coefficients of the respective state.
This can be written more concisely as
iff .
The proof is detailed in the paper and will be added here at a later date.
In quantum physics, a wave function is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ. Wave functions are composed of complex numbers. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density of measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called normalization. Since the wave function is complex-valued, only its relative phase and relative magnitude can be measured; its value does not, in isolation, tell anything about the magnitudes or directions of measurable observables. One has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.
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