About quantum measurements

Li Wei

The concept of a(A,B)-quantum measurement is introduced and discussed.An equivalent relation between(A,B)-quantum measurement and g-frame with lower and upper bounds A and B is established.Some properties of direct sums and multiplications of(A,B)-quantum measurements are obtained.The measure frame operator and the dual quantum measurement of a(A,B)-quantum measurement are introduced and its canonical dual is constructed.Finally,a reconstruction formula of a quantum states is obtained in light of a(A,B)-quantum measurement.

Art Hobson

Neal G. Anderson

Fundamental studies of quantum measurements and their capacity to acquire information are typically based on scenarios in which the full Hilbert space of the measured quantum system is open to measurement interactions. In this work, we consider a class of incomplete quantum measurements — quantum subspace measurements (QSM's) — for which all measurement interactions are restricted to an arbitrary but specified subspace of the measured system Hilbert space. We define QSM's formally through a condition on the measurement Hamiltonian, obtain forms for the post-measurement states and positive operators (POVM elements) associated with QSM's acting in a specified subspace, and upper bound the accessible information for such measurements. Characteristic features of QSM's are identified and discussed.

Pierre Meystre

Laszlo Gyongyosi, Sándor Imre

Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and the low success probability of finding a global optimal measurement output. Each measurement round requires preparing the quantum system and applying quantum operations and measurements with high-precision control in the physical layer. These issues result in extremely high-cost measurements with a low probability of success at the end of the measurement rounds. Here, we define a novel measurement for quantum computations called dense quantum measurement. The dense measurement strategy aims at fixing the main drawbacks of standard quantum measurements by achieving a significant reduction in the number of necessary measurement rounds and by radically improving the success probabilities of finding global optimal outputs. We provide application scenarios for quantum circuits with arbitrary unitary sequences, and prove that dense measurement theory provides an experimentally implementable solution for gate-model quantum computer architectures.