Quantifying entanglement in two-mode Gaussian states

Abstract

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.

arXiv comment8 pages,3 figs; The original submission gave an analytical formula that was claimed to give the entanglement of formation for arbitrary two-mode Gaussian states - this was incorrect. The formula gives a lower bound of EoF which saturates for symmetric states and for states with balanced correlations, and is a good approximation for most other states. This error is corrected in the revised version

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• Partial-transpose-guided entanglement classes and minimum noise filtering in many-body Gaussian quantum systems
• Quantum synchronization in an all-optical stroboscopic quantum simulator
• On the equivalence between squeezing and entanglement potential for two-mode Gaussian states
• Improving Continuous-variable Quantum Channels with Unitary Averaging
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• Spectral stabilizability
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• Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability
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