For any quantum observable (positive operator valued measure (POVM)), we show that its compatible quantum instruments can be identified with certain channels and can be seen as combinations of Lüders operations and channels. We prove that a POVM is rank-1 exactly when its compatible instruments are nuclear and their associate channels are entanglement-breaking. Any instrument can be maximally refined into a rank-1 instrument. We present a characterization for (minimal) pure realizations of instruments and characterize completely the minimal pure measurement models of POVMs. The standard model of quantum measurement theory is generalized for arbitrary observables. Finally, we study post measurement states.For any quantum observable (positive operator valued measure (POVM)), we show that its compatible quantum instruments can be identified with certain channels and can be seen as combinations of Lüders operations and channels. We prove that a POVM is rank-1 exactly when its compatible instruments are nuclear and their associate channels are entanglement-breaking. Any instrument can be maximally refined into a rank-1 instrument. We present a characterization for (minimal) pure realizations of instruments and characterize completely the minimal pure measurement models of POVMs. The standard model of quantum measurement theory is generalized for arbitrary observables. Finally, we study post measurement states.

arXiv:1202.5905Journal of Physics A Mathematical and TheoreticalDec 10, 201222 citations

Quantum Measurement with a Positive Operator-Valued Measure

Howard E. Brandt

Acta Physica Hungarica B) Quantum ElectronicsJan 1, 20041 citation

Positive Operator-Valued Measures in Quantum Decision Theory

Vyacheslav I. Yukalov, Didier Sornette

Lecture notes in computer scienceJan 1, 201511 citations

Construction of the least informative observable conserved by a given quantum instrument

Yui Kuramochi

For a quantum measurement process described by a quantum instrument I and a system observable corresponding to a positive-operator valued measure (POVM) E, I is said to conserve the information of E if the joint successive measurement of I followed by E is equivalent to a single measurement of E. We show that for any quantum instrument I we can construct a POVM conserved by I. Intuitively, the construction gives the infinite joint successive measurement of I. We also show that the constructed POVM is the least informative observable among POVMs conserved by I, i.e., the constructed POVM can be realized by a classical post-processing of any POVM conserved by I. As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.For a quantum measurement process described by a quantum instrument I and a system observable corresponding to a positive-operator valued measure (POVM) E, I is said to conserve the information of E if the joint successive measurement of I followed by E is equivalent to a single measurement of E. We show that for any quantum instrument I we can construct a POVM conserved by I. Intuitively, the construction gives the infinite joint successive measurement of I. We also show that the constructed POVM is the least informative observable among POVMs conserved by I, i.e., the constructed POVM can be realized by a classical post-processing of any POVM conserved by I. As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.

arXiv:1505.07232Journal of Mathematical PhysicsSep 1, 20154 citations

Construction of the least informative observable conserved by a given quantum instrument

Yui Kuramochi

For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint successive measurement of $\mathcal{I}$ followed by $E$ is equivalent to a single measurement of $E .$ We show that for any quantum instrument $\mathcal{I}$ we can construct a POVM conserved by $\mathcal{I}$ . Intuitively the construction gives the infinite joint successive measurement of $\mathcal{I}.$ We also show that the constructed POVM is the least informative observable among POVMs conserved by $\mathcal{I}$ , i.e. the constructed POVM can be realized by a classical post-processing of any POVM conserved by $\mathcal{I} .$ As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint successive measurement of $\mathcal{I}$ followed by $E$ is equivalent to a single measurement of $E .$ We show that for any quantum instrument $\mathcal{I}$ we can construct a POVM conserved by $\mathcal{I}$. Intuitively the construction gives the infinite joint successive measurement of $\mathcal{I}.$ We also show that the constructed POVM is the least informative observable among POVMs conserved by $\mathcal{I}$, i.e. the constructed POVM can be realized by a classical post-processing of any POVM conserved by $\mathcal{I} .$ As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.

Sep 28, 20153 citations

Construction of Positive-Operator Valued Measures via Wavefunctions of Physical Systems

Xuehong Wang, Yan Li, Hong-Yi Su +1 more

International Journal of Theoretical PhysicsOct 9, 20120 citations

For a quantum measurement process described by a quantum instrument

\mathcal{I}

and a system observable corresponding to a positive-operator valued measure (POVM)

E ,

\mathcal{I}

is said to conserve the information of

E

if the joint successive measurement of

\mathcal{I}

followed by

E

is equivalent to a single measurement of

E .

We show that for any quantum instrument

\mathcal{I}

we can construct a POVM conserved by

\mathcal{I}

. Intuitively the construction gives the infinite joint successive measurement of

\mathcal{I}.

We also show that the constructed POVM is the least informative observable among POVMs conserved by

\mathcal{I}

, i.e. the constructed POVM can be realized by a classical post-processing of any POVM conserved by

\mathcal{I} .

As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.