Decoherence of multidimensional entangled coherent states
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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.Keywords:
Photon entanglement
Multipartite entanglement
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양자상태의 얽힘을 양으로 나타낼 수 있는 방법들에 대하여 기술하였다. 두 부분으로 구성된 순수 양자상태는 쉽게 얽힘을 판별할 수 있는 방법을 알 수 있으나 혼합된 형태의 양자상태는 양자 얽힘을 판별하기가 어렵다. 일반적으로 부분이 많아지는 경우에 대해서는 순수 상태도 그 판별을 하는 것이 어렵다고 알려져 있으나 이 논문에서 그 방법을 제시하고 혼합 상태로의 적용에 대하여 논의한다. We present a method describing the quantum entanglement. We knows the criterion which can determine entanglement in a bipartite system. It is difficult in mixed states. Even though the entanglement criterion for multipartite systems is difficult, we offer a criterion for multiqubits and discuss entanglement of the mixed state.
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A natural way of quantifying the degree of entanglement for a pure quantum state is to compare how far this state is from the set of all unentangled pure states. This geometric measure of entanglement is explored for bipartite and multipartite pure and mixed states. It is determined analytically for arbitrary two‐qubit mixed states and for generalized Werner and isotropic states. It is also applied to certain multipartite mixed states, including two multipartite bound entangled states discovered by Smolin and Dür. Moreover, the geometric measure of entanglement is applied to the ground state of the Ising model in a transverse magnetic field. From this model the entanglement is shown to exhibit singular behavior at the quantum critical point.
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