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Conference on Lasers and Electro-Optics

Experimental Implementation of an Approximate Partial Transpose for Two-Qubit Systems

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

Published Jan 1, 2012• 1 citation

Abstract

We report the first experimental realization of an approximate partial transpose for photonic two-qubit systems. Direct detection of entanglement, i.e., without performing quantum state tomography, using the partial transpose operation, is also demonstrated.

DOI: 10.1364/qels.2012.qf3f.8

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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.