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arXiv:1006.0786 · Physical Review A

Experimental implementation of the universal transpose operation using the structural physical approximation

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

Published Feb 18, 2011• 15 citations
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Abstract

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.

DOI
10.1103/physreva.83.020301

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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.
The partial transpose by which a subsystem's quantum state is solely transposed is of unique importance in quantum information processing from both fundamental and practical point of view. In this work, we present a practical scheme to realize a physical approximation to the partial transpose using local measurements on individual quantum systems and classical communication. We then report its linear optical realization and show that the scheme works with no dependence on local basis of given quantum states. A proof-of-principle demonstration of entanglement detection using the physical approximation of the partial transpose is also reported.
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.