Related papers: Generalised quantum weakest preconditions
The indeterminism of quantum mechanics generally permits the independent specification of both an initial and a final condition on the state. Quantum pre-and-post-selection of states opens up a new, experimentally testable, sector of…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspecitve. This is done by…
We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data-processing of the outcomes of a quantum measurement described by a POVM. We determine the optimal processing that…
The notion of state reduction employed by the standard quantum theory of measurement is difficult to accept for two reasons: It leaves open where and when the reduction takes place and it does not give any objective conditions under which…
In a recent letter [Information Processing Letters~104 (2007) 152-158], it has shown some sufficient conditions for commutativity of quantum weakest preconditions. This paper provides some alternative and simple characterizations for the…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators subject to affine…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension $d$ using only classical resources and a single ancillary qubit. Our method is based on the probabilistic…
We derive a measurement operator corresponding to a quantum nondemolition (QND) measurement of an atomic ensemble. The quantum measurement operator takes the form of a positive operator valued measure (POVM) and is valid for arbitrary…
The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and…
We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalised probability operator…
It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems…
It has been shown that any generalized measurement can be decomposed into a sequence of weak measurements corresponding to a stochastic process. However, the weak measurements may require almost arbitrary unitaries, which are unlikely to be…
The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is…
We discuss a generalization of POVM which is used in quantum-like modeling of mental processing.