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Chinese Physics Letters

Quantum Decoherence for Multi-Photon Entangled States

孙艳华, 朱霞, 匡乐满

Published Jan 1, 2005• 0 citations
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Abstract

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.

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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.
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.
Quantum entanglement and quantum nonlocality of N -photon entangled states |ψ Nm ⟩ = C m [cos γ| N − m ⟩ 1 | m ⟩ 2 +e iθ m sin γ| m ⟩ 1 | N − m ⟩ 2 ] and their superpositions are studied. We point out that the relative phase θ m affects the quantum nonlocality but not the quantum entanglement for the state |ψ Nm ⟩. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |ψ Nm ⟩, superposition coefficients and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |ψ Nm ⟩ can increase the amount of entanglement and give more ways to reach the maximal violation of the Bell inequality.
In this paper we investigate the quantum decoherence and the dynamics of nonlocality of two-mode single-photon subtracted squeezed vacuum state(TSSV).We numerically calculate the relative entropy of the entanglement and analyze in detail the linear entropy of the entanglement.Then we calculate the Bell-CHSH inequality based upon pseudospin operators and find that the Bell inequality is always violated.Therefore,we are sure that the decoherence can only decrease the amount of the entanglement but can not eliminate the entanglement of TSSV completely.
Considering the interaction between two-mode SU(1,1) coherence states and a two-level atom, we find an exact solution of the Milburn equation for the system. We investigate the time evolution of the entanglement of field-atom and one of two modes of field using the quantum-reduced entropy and quantum relative entropy, respectively. The influences of intrinsic decoherence and two-mode photon number difference on the evolution of the entanglement of field-atom and one of two modes of field are discussed. It is shown that the entanglement of field-atom reduces to a stationary value with time evolution and the entanglement between two modes increases to another stationary value with intrinsic decoherence, and the values only depend on the two-mode photon number and mean photon number.
The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an alternative view of how to think about this problem. We consider mixed states of two qubits and obtain an exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (or atoms) within a perfect cavity for the case of multiphoton transition. We consider the situation for which the field may start from a binomial state. Employing this solution, the significant features of the entanglement when a second qubit is weakly coupled to the field and becomes entangled with the first qubit, is investigated. We also describe the response of the atomic system as it varies between the Rabi oscillations and the collapse–revival mode and investigate the atomic inversion and the Q -function. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement are influenced significantly when the multi-photon process is involved. Finally, we obtain illustrative examples of some novel aspects of this system and show how the off-resonant case can sensitize entanglement to the role of initial state setting.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.