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arXiv:quant-ph/0605146 · Journal of the Optical Society of America B

Selective truncations of an optical state using projection synthesis

Adam Miranowicz, Şahin Kaya Özdemir, J. Bajer, Masato Koashi, Nobuyuki Imoto

Published Jan 26, 2007• 20 citations
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Abstract

Selective truncation of the Fock-state expansion of an optical field can be achieved using projection synthesis. The process removes the predetermined Fock states from the input field by conditional measurement and teleportation. We present a scheme to perform projection synthesis based on multiport interferometry. This scheme can be used both as a generalized quantum scissors device that filters out Fock states with photon numbers higher than a predetermined value, and as a quantum punching device that selectively removes specific Fock states, making holes in the Fock-state expansion of the input field.

DOI
10.1364/josab.24.000379

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Selective truncation of the Fock-state expansion of an optical field can be achieved using projection synthesis. The process removes the predetermined Fock states from the input field by conditional measurement and teleportation. We present a scheme to perform projection synthesis based on multiport interferometry. This scheme can be used both as a generalized quantum scissors device that filters out Fock states with photon numbers higher than a predetermined value, and as a quantum punching device that selectively removes specific Fock states, making holes in the Fock-state expansion of the input field.
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The quantum scissors device of Pegg et al (1998 Phys. Rev. Lett. 81 1604) enables truncation of the Fock-state expansion of an input optical field to qubit and qutrit (three-dimensional) states only. Here, a generalized scissors device is proposed using an eight-port optical interferometer. Upon post-selection based on photon counting results, the interferometer implements generation and teleportation of qudit ( d -dimensional) states by truncation of an input field at the ( d −1)th term of its Fock-state expansion up to d = 6. Examples of selective truncations, which can be interpreted as a Fock-state filtering and hole burning in the Fock space of an input optical field, are discussed. Deterioration of the truncation due to imperfect photon counting is discussed including inefficiency, dark counts and realistic photon-number resolutions of photodetectors.
We generalize the concept of optical state truncation and noiseless linear amplification to enable truncation of the Fock-state expansion of an optical state to higher order and to simultaneously amplify it using linear optics. The resulting generalized quantum scissors are more efficient for noiseless linear amplification than employing multiple scissors in parallel and are experimentally practical. As a particular example, we focus on a third-order scissor device and demonstrate advantages in terms of fidelity with the target state, probability of success, distillable entanglement, and the amount of non-Gaussianity introduced.
We present a scheme of quantum state truncation in the Fock basis (quantum scissors), based on the combined action of a nondegenerate optical parametric amplifier and a beam splitter. Differently from previously proposed linear-optics-based quantum scissors devices, which depend on reliable Fock state sources, our scheme requires only readily available Gaussian states, such as coherent state inputs (vacuum state included). A truncated state is generated after performing photodetections in the global state. We find that, depending on which output ports each of the two photodetectors is positioned, different types of truncated states may be produced: (i) states having a maximum Fock number of NNN, or (ii) states having a minimum Fock number NNN. In order to illustrate our method, we discuss an example having as input states a coherent state in the beam splitter and vacuum states in the amplifier, and show that the resulting truncated states display nonclassical properties, such as sub-Poissonian statistics and squeezing. We quantify the nonclassicality degree of the generated states using the Wigner-Yanase skew information measure. For complementarity, we discuss the efficiency of the protocol, e.g., generation probability as well as the effects of imperfections such as the detector's quantum efficiency and dark counts rate.