Related papers: Random positive operator valued measures
The optimal measurement that discriminates nonorthogonal quantum states with fixed rates of inconclusive outcomes (FRIO) can be decomposed into an assisted separation of the inputs, yielding conclusive and inconclusive outputs, followed by…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the typical…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
A quantum measurement, often referred to as positive operator-valued measurement (POVM), is a set of positive operators $P_j=P_j^\dag\geq 0$ summing to identity, $\sum_jP_j=\mathbb{1}$. This can be seen as a generalization of a probability…
Nonunitary quantum operations generating thermostatistical states and forming positive operator-valued measures (POVMs) are of current interest as a useful tool for operational approach to quantum thermodynamics. Here, two different…
The quantum reference frames program is based on the idea that reference frames should be treated as quantum physical systems. In this work, we combine these insights with the emphasis on operationality, understood as refraining from…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by…
We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for the values of such observables can be made…
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…
We represent quantum observables as POVMs (normalized positive operator valued measures) and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group $G$.…
We study the problem of separating the data produced by a given quantum measurement (on states from a memoryless source which is unknown except for its average state), described by a positive operator valued measure (POVM), into a…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
Many quantum measurements, such as photodetection, can be destructive. In photodetection, when the detector clicks a photon has been absorbed and destroyed. Yet the lack of a click also gives information about the presence or absence of a…