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A density operator that is a rank-1 projection is known as a pure quantum state, and all quantum states that are not pure are designated mixed. Pure states are also known as wavefunctions . Assigning a pure state to a quantum system implies certainty about the outcome of some measurement on that system (i.e., P ( x ) = 1 {\displaystyle P(x)=1 ...
The standard semantics of quantum logic is that quantum logic is the logic of projection operators in a separable Hilbert or pre-Hilbert space, where an observable p is associated with the set of quantum states for which p (when measured) has eigenvalue 1. From there,
Q|SI> is a platform embedded in .Net language supporting quantum programming in a quantum extension of while-language. [ 47 ] [ 56 ] This platform includes a compiler of the quantum while-language [ 57 ] and a chain of tools for the simulation of quantum computation, optimisation of quantum circuits, termination analysis of quantum programs ...
In the context of quantum information theory, the operators {V i} are called the Kraus operators (after Karl Kraus) of Φ. Notice, given a completely positive Φ, its Kraus operators need not be unique. For example, any "square root" factorization of the Choi matrix C Φ = B ∗ B gives a set of Kraus operators. Let
A density operator is a positive-semidefinite operator on the Hilbert space whose trace is equal to 1. In the language of von Weizsäcker, a density operator is a "catalogue of probabilities": for each measurement that can be defined, the probability distribution over the outcomes of that measurement can be computed from the density operator. [2]
In quantum mechanics, given a projection-valued measure of a measurable space to the space of continuous endomorphisms upon a Hilbert space , the projective space P ( H ) {\displaystyle \mathbf {P} (H)} of the Hilbert space H {\displaystyle H} is interpreted as the set of possible ( normalizable ) states φ {\displaystyle \varphi } of a quantum ...
In functional analysis and quantum information science, a positive operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalization of projection-valued measures (PVM) and, correspondingly, quantum measurements described by POVMs are a generalization of quantum ...
In quantum mechanics, an antisymmetrizer (also known as an antisymmetrizing operator [1]) is a linear operator that makes a wave function of N identical fermions antisymmetric under the exchange of the coordinates of any pair of fermions.