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Register a new userBroadcasting of entanglement in three-particle GHZ state via quantum copying
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We introduce entanglement measures to describe entanglement in a three-particle system and apply it to studying broadcasting of entanglement in three-particle GHZ state. We show that entanglement of three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement.
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We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state via non-local cloning exhibits the fidelity better than local cloning.
Recently Yang et al. [Int. J. Theo. Phys. 48 (2009) 516] have shown that an unknown qubit can be teleported by using a particular GHZ-like state as quantum channel. However, there are several errors in the calculation which lead to incorrect conclusions. The errors have been indicated and corrected. It is also noted that their scheme and the independently proposed teleportation scheme of Zhang et al. [Int. J. Theo. Phys. 48 (2009) 3331] uses quantum channel from the same family and any state of that family may be used for teleportation.
It is known that beyond $2 otimes 2$ and $2 otimes 3$ dimensional quantum systems, Peres-Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there can exist bound entangled states as well as free entangled states. All free/useful/distillable entanglement is a part of the class of NPT entangled states. In this article, we ask the question that given an NPT entangled state in $3 otimes3$ dimensional system as a resource, how much entanglement can we broadcast so that resource still remains NPT. We have chosen $3 otimes 3$ system as a first step to understand broadcasting of NPT states in higher dimensional systems. In particular, we find out the range of broadcasting of NPT entanglement for Two parameter Class of States (TPCS) and Isotropic States (IS). Interestingly, as a derivative of this process we are also able to locate the existence of absolute PPT states (ABPPT) in $3 otimes 3$ dimensional system. Here we implement the strategy of broadcasting through approximate cloning operations.
A scheme for arbitrary quantum state engineering (QSE) in three-state systems is proposed. Firstly, starting from a set of complete orthogonal time-dependent basis with undetermined coefficients, a time-dependent Hamiltonian is derived via Counterdiabatic driving for the purpose of guiding the system to attain an arbitrary target state at a predefined time. Then, on request of the assumed target states, two single-mode driving protocols and a multi-mode driving protocol are proposed as examples to discuss the validity of the QSE scheme. The result of comparison between single-mode driving and multi-mode driving shows that multi-mode driving seems to have a wider rang of application prospect because it can drive the system to an arbitrary target state from an arbitrary initial state also at a predefined time even without the use of microwave fields for the transition between the two ground states. Moreover, for the purpose of discussion in the schemes feasibility in practice, a polynomial ansatz as the simplest exampleis used to fix the pulses. The result shows that the pulses designed to implement the protocols are not hard to be realized in practice. At the end, QSE in higher-dimensional systems is also discussed in brief as a generalization example of the scheme.
We present an entanglement swapping process for unknown nonmaximally entangled photonic states, where the standard Bell-state measurement is replaced by a three-step quantum walk-like state discrimination process, i.e., the practically nontrivial coupling element of two photons is replaced by manipulating their trajectories, which will greatly enrich the dynamics of the coupling between photons in realizing quantum computation, and reduce the integration complexity of optical quantum processing. In addition, the output state can be maximally entangled, which allows for entanglement concentration as well.
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