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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 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.
If we want to have the parity information of a valid quantum observable U, we need to apply the controlled-U gates between the ancilla qubit and the data qubits sequentially. For example, for making parity check measurement in the X basis, we need to apply CNOT gates between the ancilla qubit and the data qubits sequentially since the ...
One important aspect of quantum mechanics is the occurrence of—in general—non-commuting operators which represent observables, quantities that can be measured. A standard example of a set of such operators are the three components of the angular momentum operators, which are crucial in many quantum systems. These operators are complicated ...