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arXiv:1706.06273 · Journal of Physics Communications

Positive impact of decoherence on spin squeezing in GHZ and W states

Kapil K. Sharma, Swaroop Ganguly

Published Nov 28, 2017• 2 citations
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Abstract

We study spin squeezing behaviour in tripartite unsqueezed maximally entangled Greenberger–Horne–Zeilinger (GHZ) and W states under various decoherence channels with Kitagawa–Ueda criteria. In order to search spin squeezing sudden death (SSSD) and perform the analysis of spin squeezing production we use bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels in the present study. In literature, the influence of decoherence has been studied usually as a destroying element. On the contrary here we investigate the positive impact of decoherence, which produces spin squeezing in unsqueezed GHZ and W states under certain channels. Our careful study shows that GHZ state remains unsqueezed under aforementioned channels except bit-phase-flip and depolarization channels, on the other hand all the decoherence channels produce spin squeezing in W state. So we find that, GHZ is more robust in comparison to W state in the sense of spin squeezing production under decoherence. Most importantly we find, none of the decoherence channels produce SSSD in either of the states.

DOI
10.1088/2399-6528/aa9dac

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We study spin squeezing behaviour in tripartite unsqueezed maximally entangled Greenberger–Horne–Zeilinger (GHZ) and W states under various decoherence channels with Kitagawa–Ueda criteria. In order to search spin squeezing sudden death (SSSD) and perform the analysis of spin squeezing production we use bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels in the present study. In literature, the influence of decoherence has been studied usually as a destroying element. On the contrary here we investigate the positive impact of decoherence, which produces spin squeezing in unsqueezed GHZ and W states under certain channels. Our careful study shows that GHZ state remains unsqueezed under aforementioned channels except bit-phase-flip and depolarization channels, on the other hand all the decoherence channels produce spin squeezing in W state. So we find that, GHZ is more robust in comparison to W state in the sense of spin squeezing production under decoherence. Most importantly we find, none of the decoherence channels produce SSSD in either of the states.
The one-tangle and π-tangle are used to quantify the entanglement of a tripartite Greenberger–Horne–Zeilinger (GHZ) state in non-inertial frames when the system interacts with a noisy environment in the form of phase damping, phase flip and bit flip channels. It is shown that the two-tangles behave as a closed system. The one-tangle and π-tangle have different behaviors in the three channels. In the case of the phase damping channel, depending on the kind of coupling, the sudden death of both the one-tangle and π-tangle may or may not happen, whereas in the case of the phase flip channel the sudden death cannot be avoided. The effect of decoherence may be ignored in the limit of infinite acceleration when the system interacts with a bit flip channel. Furthermore, a sudden rebirth of the one-tangle and π-tangle occurs in the case of the phase flip channel which may be delayed when collective coupling is switched on.
In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of super-position and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel performs well for spin squeezing generation and generates permanent spin squeezing in the superposition of GHZ and W states.
In order to witness multipartite correlations beyond pairwise entanglement, spin-squeezing parameters are analytically calculated for a spin ensemble in a collective initial state under three different decoherence channels. It is shown that, in analogy to pairwise entanglement, the spin squeezing described by different parameters can suddenly become zero at different vanishing times. This finding shows the general occurrence of sudden vanishing phenomena of quantum correlations in many-body systems, which here is referred to as spin-squeezing sudden death (SSSD). It is shown that the SSSD usually occurs due to decoherence and that SSSD never occurs for some initial states in the amplitude-damping channel. We also analytically obtain the vanishing times of spin squeezing.
The decoherence effect on multipartite entanglement in non-inertial frames is investigated. The GHZ state is considered to be shared between partners with one partner in the inertial frame whereas the other two are in accelerated frames. One-tangle and π-tangles are used to quantify the entanglement of the multipartite system influenced by phase damping and phase flip channels. It is seen that for the phase damping channel, entanglement sudden death (ESD) occurs for p > 0.5 in the infinite acceleration limit. On the other hand, in the case of the phase flip channel, ESD behavior occurs at p = 0.5. It is also seen that entanglement sudden birth (ESB) occurs in the case of phase flip channel just after ESD, i.e. p > 0.5. Furthermore, it is seen that the effect of the environment on multipartite entanglement is much stronger than that of the acceleration of non-inertial frames.
We study the spin-squeezing property of weighted graph states, which can be used to improve the sensitivity in interferometry. Decoherence reduces the spin-squeezing property but the result remains superior over other reference schemes with Greenberger-Horne-Zeilinger (GHZ) type maximally entangled states and product states. We study the time evolution of spin squeezing of weighted graph states coupled to different decoherence channels. Based on the analysis, the spin squeezing of the weighted graph states is robust in the presence of decoherence, and the decoherence limit in the improvement of the interferometric sensitivity is still achievable.
In this article the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits and profound impact of DM interaction is studied on the initial entanglement of the system. As a result we find that the bipartite partitions of W states suffer from entanglement sudden death (i.e. ESD), while tripartite entanglement does not. On the other hand bipartite partitions and tripartite entanglement in GHZ states does not feel any influence of DM interaction. So, we find that GHZ states have robust character than W states. In this work we consider generalised GHZ and W states and three πππ is used as an entanglement measure. This study can be useful in quantum information processing where unwanted DM interaction takes place.