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arXiv:quant-ph/0503207 · Physical Review A

Decoherence of multidimensional entangled coherent states

S. J. van Enk

Published Aug 12, 2005• 36 citations
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Abstract

For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multidimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement $E$ provided the number of photons is at least of order ${2}^{2E}$. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equal to $2∕\mathrm{ln}(2)\ensuremath{\approx}2.89$ ebits per absorbed photon, irrespective of the amount of pure-state entanglement $E$ one started with. In contrast, for larger losses it tends to be the remaining amount of entanglement that is independent of $E$. This may provide a useful strategy for creating states with a fixed amount of entanglement.

DOI
10.1103/physreva.72.022308

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For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multidimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement EEE provided the number of photons is at least of order 22E{2}^{2E}22E. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equal to 2∕ln(2)\ensuremath≈2.892∕\mathrm{ln}(2)\ensuremath{\approx}2.892∕ln(2)\ensuremath≈2.89 ebits per absorbed photon, irrespective of the amount of pure-state entanglement EEE one started with. In contrast, for larger losses it tends to be the remaining amount of entanglement that is independent of EEE. This may provide a useful strategy for creating states with a fixed amount of entanglement.
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.
The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied, with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices, the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement. In particular, they do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure.
We investigate quantum decoherence of the multi-photon entangled state |ψ Nm ⟩ = m [cos γ| N − m ⟩ 1 | m ⟩ 2 + e i θ m sin γ| m ⟩ 1 | N − m ⟩ 2 ]. When the entangled channel |ψ Nm ⟩ is embedded in an environment, the channel decoheres and becomes a mixed state governed by a master equation. We calculate the linear entropy and the relative entropy of entanglement, which describe the mixedness and the amount of entanglement for the mixed state, respectively. We show that quantum decoherence weakens the amount of entanglement and enhances the mixedness with the time evolution. It is indicated that the relative entropy of entanglement depends on not only the initial entanglement angle and the decohering parameter, but also the number of photons in each mode. In particular, we find that the decohering speed depends on the number-difference of photons in the two modes. The larger the number-difference of photons is, the higher the decohering speed.
We investigate quantum decoherence of the multi-photon entangled state |ψNm) = Nm [cosγ|N - m>1|m)2 +e^iθm sinγ|m>1|N-m>2]. When the entangled channel |ψNm) is embedded in an environment, the channel decoheres and becomes a mixed state governed by a master equation. We calculate the linear entropy and the relative entropy of entanglement, which describe the mixedness and the amount of entanglement for the mixed state, respectively. We show that quantum decoherence weakens the amount of entanglement and enhances the mixedness with the time evolution. It is indicated that the relative entropy of entanglement depends on not only the initial entanglement angle and the decohering parameter, but also the number of photons in each mode. In particular, we find that the decohering speed depends on the number-difference of photons in the two modes. The larger the number-difference of photons is, the higher the decohering speed.
Polarization of light has been used extensively in quantum information processing, and quantum entanglement is essential to many areas of research, including quantum computing. Here we investigate the degree of polarization and the entanglement of a family of quantum states known as photon-added entangled coherent states. Such states could serve as means of entanglement distribution and quantum key distribution. Using the quantum Stokes parameters and the QQQ function, we demonstrate that, in general, the degree of polarization of two two-mode photon-added coherent states increases significantly with the number of added photons. And using the concurrence, we show that the amount of entanglement in this kind of superposition presents a behavior that is dependent on whether or not the number of added photons in each mode is the same.