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Experimental implementation of the universal transpose operation using structural physical approximation

Hyang‐Tag Lim, Young-Sik Ra, Yong‐Su Kim, Joonwoo Bae, Yoon-Ho Kim

Published Jan 1, 2011• 1 citation
Publisher

Abstract

We investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics.
DOI
10.1364/qels.2011.qtho4

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The universal transpose of quantum states is an antiunitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as structural physical approximation. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained, and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as structural physical approximation. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained, and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
Although important for detecting entanglement, the transpose operation cannot be directly realized in laboratory because it is a nonphysical operation. It is, however, possible to find an approximate transpose operation using the method known as the structural physical approximation (SPA); recently, SPA-based implementations of the transpose and partial transpose have been demonstrated for a single-qubit [Phys. Rev. A 83, 020301(R) (2011)] and an entangled two-qubit system [Phys. Rev. Lett. 107, 160401 (2011)]. In this work, we expand SPA-transpose to a three-dimensional quantum system: a qutrit. The photonic qutrit state is encoded in the polarization, and path degrees of freedom of a single-photon and the SPA-transpose operation, which is based on measurement and preparation of quantum states, is implemented with linear optics. Our work paves the way toward entanglement detection for higher-dimensional quantum systems.