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Chinese Physics B

Quantum entanglement of an entangled coherent state: Role of particle losses

Pan Liu, Xiao-Min Feng, Guangri Jin

Published Mar 1, 2014• 3 citations
Publisher

Abstract

We analyze entanglement properties of entangled coherent state (ECS), |α, 0〉 1,2 + |0, α〉 1,2 , with and without photon losses. By separating the coherent state into , we derive exact results of the logarithmic negativity E N , which quantifies the degree of entanglement between the two bosonic modes. Without particle losses, E N = 1 for the N00N state; while for the ECS, E N increases from 0 to 1 as |α| 2 → ∞ . In the presence of photon losses, we find that the ECS with large enough photon number is more robust than that of the N00N state. An optimal ECS is obtained by maximizing E N with respect to |α| 2 .

DOI
10.1088/1674-1056/23/3/030310

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We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.
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We study the effects of losses on the entanglement created between two separate atomic gases by optical probing and homodyne detection of the transmitted light. The system is well-described in the Gaussian state formulation. Analytical results quantifying the degree of entanglement between the two gases are derived and compared with the entanglement in a pair of light pulses generated by an Einstein-Podolsky-Rosen (EPR) source. For low (high) transmission losses, the highest degree of entanglement is obtained by probing with squeezed (antisqueezed) light. In an asymmetric setup where light is only sent one way through the atomic samples, we find that the logarithmic negativity of entanglement attains a constant value $\ensuremath{-}{\mathrm{log}}_{2}(N)$ with N=1∕3N=1∕3N=1∕3, irrespective of the loss along the transmission line.
We investigate the performance of entangled coherent states for quantum-enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.