The Role of Entanglement in Quantum Information Processing

The Role of Entanglement in Quantum Information Processing

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Entanglement plays an important role in Quantum Information Processing. It has wide applications in areas of Quantum cryptography, secure communications, teleportation and so on. All these protocols involve muti party entanglement which requires locally producing the entanglement and then distributing it to different parties. These multiparticle entanglement can be of various types depending upon its number of qubits. Interestingly upon distribution the states will interact with the environment and become mixed state or less entangled pure state. For proper execution of most of the protocols we need a perfect channel thus we need to convert the non maximally entangled state back into maximally entangled state. The transformation of a less entangled pure state (pure non maximally entangled state) into a maximally entangled state is known as entanglement concentration whereas transformation of a mixed non-maximally entangled state into a maximally entangled state is known as entanglement purification/distillation. In 1996 Bennet et al. [origional ECP] proposed the first entanglement concentration protocol by using collective entanglement concentration procedure (known as Schmidt projective method).

Recently many schemes for the ECPs and the EPs are implemented for different states such as Bennet et al. [EP] implemented ECP for bell state, Sheng et al. [Sheng-1] impemented ECP for maximally entangled Bell state, Sheng et al. [Sheng-2] impemented ECP for arbitrary W state, Bose et al. [S. Bose ] impemented ECP based on entanglement swapping (needs collective Bell state measurement) for maximally entangled Bell state, Chaudhury and Dhara have implemented ECP for GHZ [Dhara GHZ state] and Cluster state [Dhara Cluster state], Zhou et al. [NOON] for NOON states etc. But we are interested in entanglement concentration for Cat state and GHZ-like state using non-maximally entangled Bell state via a special kind of circuit through which the scheme for the construction of pure maximally entangled state is proposed.

Interestingly, up to date different techniques/strategies have been used for realization of the protocols of entanglement concentration (ECPs) and entanglement purification (EPs) or distillation, such as linear optics (use of PBSs), cross-Kerr-nonlinearities (use of QNDs), purification via entanglement swapping, unitary transformation [unitarytranx] and quantum electrodynamics (QED) techniques [QED] etc.

Rest of the paper is organized as follows: In Section [sec:Entanglement-concentration-protocols] our scheme is presented for Cat state and GHZ-like state with their respective circuits, Section [sec:Efficiency] efficiency part is discussed and finally the paper is concluded in Section [sec:Conclusion].

Physica A 337 (2004) 141 – 148=>Vedral et al. proposed the three

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basic steps needed by general entanglement puri2cation protocols: (1) the local general measurements on the total system; (2) the classical communication; (3) postselection: the selection of the entangled pairs with higher purity conditioned on the measurement result of subsystems [21].

Optics Communications 284 (2011) 2402=>degradation of entanglement is unavoidable during storing, processing and transmission processes. As entanglement cannot be increased by local operations and classical communication (LOCC) [5], entanglement purification will be essential for the best performances of quantum communication and quantum computation. Entanglement purification is a process that one can extract a certain number of almost perfectly entangled states froma large number of less entangled states using LOCC. For the pure nonmaximally entangled states case, this process will be called entanglement concentration. In 1996, Bennett et al. [6] proposed the first concentration protocol for identical partially entangled pairs of two-state particles where the two parties of quantum communication need to perform a collective and nondestructive measurement for the joint state of n pairs of qubits; unfortunately, this scheme is hard to implement in practice because so many particles are needed to measure simultaneously. Bose et al. [7] presented another concentration scheme of polarization entangled photons via entanglement swapping. After that, a lot of authors have been devoted to polarization entanglement concentration using by linear optical elements and collective Bell-statemeasurement [8–11] or by nonlinear optics and quantum nondemolition detector [12].

Entanglement purification deals with mixed entangled states, distilling a subsetsystem with high fidelity entanglement from a mixed entangled ensemble [13–24], while entanglement concentration is used to extract the maximally entangled state from a partially entangled pure state. Though entanglement purification can be used to purify mixed states, entanglement concentration is of interest in its own rights. As entanglement concentration protocols (ECPs) provide us a way to generate maximally entangled states, while entanglement purification protocols (EPPs) only generate highlye ntangled states by consuming more than half the quantum resource in each round.

PhysicaB404(2009)1917–1919=> The main idea of entanglement purification is that one obtains comparatively few entangled pairs, the entanglement of which will be enhanced, from many nonmaximally entangled pairs by local operations and classical communication (LOCC).

Dhara=>Entanglement concentration is helpful for decoherence of entanglement which arises from the storage process or the imperfect entanglement source.
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