Abstract
Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M-mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.
Highlights
The mode shift symmetry of the discrete Fourier transform (DFT) converts a cyclic shift of the input mode indices into a well-defined phase shift of the output modes. This useful property of the modes can be applied directly to the transformation of photon number states, resulting in a simple relation between the two representations of the quantum state which we call the mode shift rule of DFTs. This mode shift rule identifies the quantum coherences between different input photon numbers of the DFT with sets of photon number distributions in the output, allowing us to identify the effects of quantum coherences in the entangled input state on the correlations between photon number patterns observed after the DFT has been applied to both multi-mode systems
The observation of a specific Kvalue has direct implications for the quantum coherence between different input photon number states. We summarize these results by formulating the mode shift rule of DFTs, which states that the K-values of photon number distributions n obtained in the output of a DFT always distinguish the different eigenspaces of a mode shift operation in the input
We have presented a practical method of evaluating the entanglement between two local multi-mode systems that can be generated and scaled up if sufficiently reliable single photon sources and linear optics circuits are available
Summary
The development of large scale quantum information processing in quantum optics systems [1,2,3,4,5,6,7,8,9] can be achieved by combining the non-classical optical fields generated by single photon sources [10,11,12,13,14,15,16,17,18,19,20] with increasingly complex networks of multi-mode interferometers [21,22,23,24,25,26,27,28]. This mode shift rule identifies the quantum coherences between different input photon numbers of the DFT with sets of photon number distributions in the output, allowing us to identify the effects of quantum coherences in the entangled input state on the correlations between photon number patterns observed after the DFT has been applied to both multi-mode systems Based on this fundamental insight into the relation between photon number distributions before and after the DFT, we can derive experimental criteria for the verification of entanglement between two multi-mode systems of arbitrary size and photon numbers.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
