Characterization of conditional state-engineering quantum processes by coherent state quantum process tomography

Abstract

Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation depends on a number of system parameters. Here we experimentally examine Fock state filtration, a canonical example of a broad class of conditional quantum operations acting on a single optical field mode. This operation is based upon interference of the mode to be manipulated with an auxiliary single-photon state at a beam splitter, resulting in the entanglement of the two output modes. A conditional projective measurement onto a single photon state at one output mode heralds the success of the process. This operation, which implements a measurement-induced nonlinearity, is capable of suppressing particular photon-number probability amplitudes of an arbitrary quantum state. We employ coherent-state process tomography to determine the precise operation realized in our experiment, which is mathematically represented by a process tensor. To identify the key sources of experimental imperfection, we develop a realistic model of the process and identify three main contributions that significantly hamper its efficacy. The experimentally reconstructed process tensor is compared with the model, yielding a fidelity better than 0.95. This enables us to identify three key challenges to overcome in realizing a filter with optimal performance-namely the single-photon nature of the auxiliary state, high mode overlap of the optical fields involved, and the need for photon-number-resolving detection when heralding. The results show that the filter does indeed exhibit a non-linear response as a function of input photon number and preserves the phase relation between Fock layers of the output state, providing promise for future applications.

Qubit-Programmable Operations on Quantum Light Fields

“…In fact, the detection can not discriminate perfectly between different photon-number states, resulting in an incoherent mixture of distinct contributions. This is similar to the heralding effects on conditional operations found recently in Fock-state filtration 50 . The sheer effect is a reduction of the maximal photon number at which a satisfactory fidelity can be found with respect the results reported in Fig.…”

Scalable Generation of Multi-mode NOON States for Quantum Multiple-phase Estimation

“…The studies on FSF imperfection involve multiple variables, such as the input photon distributions, the single photon generation rate, the FSF sensitivity k (used to filter out |k〉), and the photon detection sensitivity, where its efficiency cannot be simply characterized. In 2015, an experimental model of an imperfect FSF was proposed and studied from three aspects 32 : the use of photon detectors that cannot distinguish events between one photon detection and higher-photon-number detection, the imperfect single photon catalyst that is actually a superposition of a single photon state and a vacuum state, and mode mismatch between the input state and the single photon catalyst; and they calculated the success probability of an imperfect FSF that can filter out |1〉 from a coherent state using Eq. (14) in that paper 32 .…”

“…In 2015, an experimental model of an imperfect FSF was proposed and studied from three aspects 32 : the use of photon detectors that cannot distinguish events between one photon detection and higher-photon-number detection, the imperfect single photon catalyst that is actually a superposition of a single photon state and a vacuum state, and mode mismatch between the input state and the single photon catalyst; and they calculated the success probability of an imperfect FSF that can filter out |1〉 from a coherent state using Eq. (14) in that paper 32 . This structure can be utilized to study the FSF efficiency p FSF (k) with other photon number sensitivity k, which is one of the next research directions based on the theoretical work here.…”

Quantum process tomography via completely positive and trace-preserving projection

“…continuous variable) systems, according to the formulation by Anis and Lvovsky [40]. Cooper et al reported that the algorithm ran for 6.5 hours (with a machine precision stopping rule) to reconstruct a d = 6 conditional state engineering process [41]. Fedorov et al performed QPT of a beamsplitter, revealing the Hong-Ou-Mandel effect [42].…”