Circuit analysis of quantum measurement

Abstract

We develop a circuit theory that enables us to analyze quantum measurements on a two-level system and on a continuous-variable system on an equal footing. As a measurement scheme applicable to both systems, we discuss a swapping state measurement which exchanges quantum states between the system and the measuring apparatus before the apparatus meter is read out. This swapping state measurement has an advantage in gravitational-wave detection over contractive state measurement in that the postmeasurement state of the system can be set to a prescribed one, regardless of the outcome of the measurement.

Measurement schemes for the spin quadratures on an ensemble of atoms

“…In particular, optical accessibility and coherent properties of the atomic ensembles are thought to be useful for implementing quantum memory of light and constructing a quantum interface to transfer the quantum state between the light and atoms [5,6,7,8,9,10,11].In order to construct a quantum interface, one of the central atom-light interaction is the Faraday-Rotation (FR) interaction [6,12]. On one hand, this interaction provides a two-mode-coupling gate to essentially implement any quadratic Hamiltonian interaction [13,14]. While the design of the interaction Hamiltonian and achievable fidelities in the gate operations of interface are widely investigated as well as generation schemes of quantum entanglement [4,15], how to estimate such a gate operations experimentally is less concerned [11,16,17,18].…”

“…For instance, the light quadrature of the first passage s y ′ ≃ s y +j z implies that the measurement of s y ′ yields the quadrature distribution of j z provided that the initial light state is infinite squeezed vacuum, s.t., ∆s y → 0 and s y =0. This measurement corresponds to the indirect measurement introduced by von Neumann [14,20]. Detailed description of measurement schemes associated with a single passage can be found in [8,9,19].…”

“…In the recent proposal [11] (see also [13,14]), a swapping gate that exchanges (s y , s z ) and (j y , j z ) can be implemented by the three passages of the light through the atomic-spin ensemble as in FIG. 1 (a).…”

“…It is known that the two-pass scheme depicted in FIG. 2 partially exchanges the quadratures [5,11,13,14]. The first passage in z direction and the second passage in y direction of the light transform the pair of the quadratures as (s y ′ , s z ′ , j y ′ , j z ′ ) = U † z (s y , s z , j y , j z )U z ≃ (s y + j z , s z , j y + s z , j z ) and (s y ′′ , s z ′′ , j y ′′ , j z ′′ ) = U † y ′ (s y ′ , s z ′ , j y ′ , j z ′ )U z ≃ (s y + j z , −j y , j y + s z , −s y ), respectively.…”

“…Hence, the partial swapping together with the phase shifter enables us to perform the homodyne tomography to reconstruct the spin state. The two-pass interaction is referred to as the noiseless quadrature transducer [22] associated with the contractive state measurement [14,21,23]. If we fold this two-pass scheme exploiting the FMPS then we have a simpler scheme for the homodyne tomography of the spin state with one DL and two interactions with a counter propagation as in FIG.…”