Entangling quantum measurements and their properties

Abstract

We study the mathematical structure of superoperators describing quantum measurements, including the entangling measurement-the generalization of the standard quantum measurement that results in entanglement between the measurable system and apparatus. It is shown that the coherent information can be effectively used for the analysis of such entangling measurements whose possible applications are discussed as well.

Physical implementation of entangling quantum measurements

“…with the entanglement matrix (R ij ) ≥ 0, R ii ≡ 1 [5], which is a particular case of the invariant superoperator (3). The resulted state after its action does not depend on an initial state of the system B and with the help of (4) the corresponding extended entangling measurement superoperator has the form:…”

“…Respectively, E + k Î = |k k| = Î (see, for instance, [3]). The substitution symbol ⊙ is to be substituted by a transformed operator, which is simply the density matrices in our case [4,5]; index k enumerates the eigen vectors of the measured physical variable, which is described by the operator  = λ k |k k| in the Hilbert space H A of the measured object. The generalized measurement, which is carried out in the extended space H A ⊗H a of the initial and auxiliary systems, is described by the PSM of the general form E k = Fk ⊙ F + k in the linear space of operators in H A .…”

“…The respective most general abridged notation for the ideal quantum measurement transformation in the object-apparatus system is given by the entangling quantum measurement superoperator [5]. This entangling quantum measurement can be considered as a combination of the completely coherent measurement, which provides the measurement results in a form of quantum entanglement between the apparatus and the object, and additional transformation dephasing the states of the apparatus…”

“…Definition of quantum measurement considered in Ref. [5] is based on the natural interpretation of the quantum measurement as the transformation, which is invariant with regard to the initial state of the apparatus. However, in a wide range of experimental situations [8][9][10][11] the quantum measurement transformations are applied to a bipartite system when the initial state of one of the subsystems is explicitly known (it can be, for example, the ground or specially prepared quantum state of an atom or non-excited resonator mode).…”

Quantum Measurements As a Control Resource

“…Quantum measurements are commonly used to extract information about the measured system [1] that can then be used to control the system via feedback [2,3]. However, quantum measurements also typically affect the system through the measurement's back-action that can be directly used to manipulate the system dynamics even if the measurement results are not recorded [4,5,6,7,8,9]. A manifestation of such control is the quantum anti-Zeno effect, where continuous observation of certain time-dependent operators steers the system dynamics along a predefined pathway [10,11].…”