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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,
The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.
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 ...
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 ...
By means of a projection operator, the dynamics is split into a slow, collective part (relevant part) and a rapidly fluctuating irrelevant part. The goal is to develop dynamical equations for the collective part. The Nakajima-Zwanzig (NZ) generalized master equation is a formally exact approach for simulating quantum dynamics in condensed phases.
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.
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 ...