Related papers: Post-processing minimal joint observables
Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
We consider joint measurement of two and three unsharp qubit observables through an Arthur-Kelly type joint measurement model for qubits. We investigate the effect of initial state of the detectors on the unsharpness of the measurement as…
Whereas complementarity manifests itself via two incompatible observables, quantum contextuality can only be revealed via the joint measurements among at least three observables. By incorporating unsharp measurements and joint measurements…
Chained correlation inequalities involving pairwise correlations of qubit observables in the equatorial plane are constructed based on the positivity of a sequence of moment matrices. When a jointly measurable set of fuzzy POVMs is employed…
This paper extends previous results on constructing a direct coupling quantum observer for a quantum harmonic oscillator system. In this case, we consider a complex linear quantum system plant consisting of a network of quantum harmonic…
We present a single inequality as the necessary and sufficient condition for two unsharp observables of a two-level system to be jointly measurable in a single apparatus and construct explicitly the joint observables. A complementarity…
Sequential minimum optimization is a machine-learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This…
We develop a technique to find simultaneous measurements for noisy quantum observables in finite-dimensional Hilbert spaces. We use the method to derive lower bounds for the noise needed to make incompatible measurements jointly measurable.…
Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
In quantum theory, there exist sets of operations that cannot be performed simultaneously. These sets of operations are referred to as incompatible. While this definition of incompatibility extends to general probabilistic theories (GPTs),…
In this work, we study the minimal normal measurement models of quantum instruments. We show that usually the apparatus' Hilbert space in such a model is unitarily isomorphic to the minimal Stinespring dilation space of the…
This article introduces the concepts of multi-observables and multi-instruments in quantum mechanics. A multi-observable $A$ (multi-instrument $\mathcal{I}$) has an outcome space of the form $\Omega =\Omega _1\times\cdots\times\Omega _n$…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
We explore the possibility of achieving optimal joint measurements of noncommuting observables on a single quantum system by performing conventional measurements of commuting self adjoint operators on optimal clones of the original quantum…
In the standard quantum theory, one can measure precisely only a subset of the incompatible observables. It results in lack of a formal joint probability defining objective realism even if we accept nonlocal or certain faster-than-light…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be…