Multipartite entangled magnon states as quantum communication channels

Abstract

We explicate conditions under which, the two magnon state becomes highly entangled and is useful for several quantum communication protocols. This state, which is experimentally realizable in quantum dots using Heisenberg exchange interaction, is found to be suitable for carrying out deterministic teleportation of an arbitrary two qubit composite system. Further, conditions for which the channel capacity reaches "Holevo bound", allowing maximal amount of classical information to be encoded, are derived. Later, an explicit protocol for the splitting and sharing of a two qubit entangled state among two parties, using this state as an entangled resource, is demonstrated. PACS numbers: Keywords:Entanglement, an entirely quantum mechanical phenomenon, has been a subject of intense research, since the days of Schrödinger [1] and Einstein [2]. In recent times, it has received renewed attention with the advent of quantum information processing [3]. The amalgamation of the principles of quantum entanglement and information theory has led to the possibility of carrying out tasks, which would have been otherwise impossible in the classical world [4,5]. The fact that some of the finite dimensional spin states naturally occur in physical systems and these can be experimentally realized makes them the states of choice for explicating quantum protocols [6]. The search for physically occurring entangled systems, which can be used for carrying out these quantum tasks, is of interest to both theorists and experimentalists.A natural system attracting considerable interest is that of spin chains, where the Heisenberg exchange interaction can create desired entangled states [7]. Quantum dots have also shown considerable promise in the realization of these states, which can be manipulated by varying the voltage applied through gate electrodes between adjacent quantum dots [8]. Interestingly, entanglement has been found to be retained even up to certain non-vanishing temperature. Entangled states e.g., Bell states |φ ± = 1 √ 2, (|01 ± |10 ) multipartite cluster states [7,9]:have found application in carrying out various quantum tasks like error correction [9] and state sharing [10]. In a spin chain, low lying magnon excitations of the ground state can show robust entanglement properties. In fact, the well known Bell states and W states of the form [11,12,13] are natural one magnon states, above the ferromagnetic ground states formed of two and three particles respectively. Although Bell states can be used for achieving perfect teleportation of, |ψ 1 = α|0 + β|1 , (α, β ∈ C, |α| 2 + |β| 2 = 1) the symmetric W states cannot be used. However, |W ′ can be used for the perfect teleportation of |ψ 1 in the case where |α| 2 + |β| 2 = |γ| 2 . Hence, the characterization of different multipartite magnon states need careful investigation for diverse quantum tasks. In this paper, we systematically investigate the four qubit, two magnon state for its ability to carry out various quantum tasks like teleportation, state sharing and dense coding. We...

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