Transferring entangled states through spin chains by boundary-state multiplets

Abstract

Quantum spin chains may be used to transfer quantum states between elements of a quantum information processing device. A scheme discovered recently [1] was shown to have favorable transfer properties for single-qubit states even in the presence of built-in static disorder caused by manufacturing errors. We extend that scheme in a way suggested already in [1] and study the transfer of the four Bell states which form a maximally entangled basis in the two-qubit Hilbert space. We show that perfect transfer of all four Bell states separately and of arbitrary linear combinations may be achieved for chains with hundreds of spins. For simplicity we restrict ourselves to systems without disorder.PACS numbers: 03.67. Hk, 75.10.Pq, 75.40.Gb Quantum information processing [2] relies on a number of key elements of technology, among them quantum bits and quantum gates. Since any quantum computer will contain a large number of different quantum gates and registers, information must be transferred between these elements of the computer. One possibility for that information transfer is offered by quantum spin chains, linear arrays of suitably coupled qubits. Research on quantum information transfer by spin chains started roughly a decade ago [3] and quickly developed into an active field with many contributors (see, for example, the reviews in [4]). However, most of the research up to now has focused on the transfer of single-qubit states, although the handling of entangled multi-qubit states is of primary importance in all known algorithms of quantum information processing. In this Brief Report we show how a natural extension of a single-qubit state transfer protocol [1] can be used to achieve high-fidelity transmission of arbitrary pure two-qubit states along spin chains with up to hundreds of sites.Spin chains for quantum information transfer mostly fall into one of two classes distinguished by the degree of "engineering", or fine-tuning, of the nearest-neighbor couplings along the chain. Perfect state transfer (PST) may be achieved if all transition frequencies generated by the spin chain Hamiltonian are commensurate and hence the time evolution of arbitrary initial states becomes periodic. In combination with spatial symmetry this enables perfect "mirroring" of initial states located at one end of the chain [5][6][7][8][9]. To achieve this goal, all nearest-neighbor couplings must be tuned to specific values, hence this class of chains may be called "fully engineered". A much simpler route to good (but not perfect) state transfer is opened by modifying only the boundary couplings affecting the very first and last spins of the chain, respectively, leaving all other couplings at one and the same value [10][11][12]. In the limit of weak boundary couplings the system then possesses nearly degenerate (symmetric and antisymmetric) eigenstates concentrated on the boundary spins and the dynamics of these states may be exploited for the transfer of quantum information. That class of systems may be called boundarydominated or op...

Transfer of arbitrary two-qubit states via a spin chain

“…In many cases, the adopted strategies consist of extensions of 1-QST protocols and, as a consequence, the drawbacks and inconveniences they already presented for the 1-QST are, to some extent, even more amplified when it comes to the n-QST case. For example, the multirail scheme [33,34] requires the use of several quantum spin- 1 2 chains and a complex encoding and decoding scheme of the quantum states; employing linear chains made of spins of higher dimensionality reduces the number of chains to 1 but still requires a repeated measurement process with consecutive single site operations [35]; the fully engineered chain (eventually combined with the ballistic or Rabi-like mechanism), as well as the uniformly coupled chain with specific conditions on its length, needs conditional quantum gates to be performed on the recipients of the quantum state [36][37][38]. Therefore, simpler many qubits QST schemes would be quite appealing.…”

Remote one-qubit-state control using the pure initial state of a two-qubit sender: Selective-region and eigenvalue creation

“…However, this type of remote state creation is not completely controlled by the local parameters of the sender's initial state since the required time instant (as a control parameter) must be transmitted to the receiver's side, which complicates the communication. To avoid this complication, we involve the variable parameter α 2 in the initial state (23,36). In this case, the large region of the receiver's state space can be created at the properly fixed time instant thus making the remote state creation completely controlled by the local sender's initial state (the local control of state-creation), because the above time instant of state registration can be reported to the receiver's side in advance.…”

“…( 23)) and by the parameters of unitary transformation (25) of the ground sender's state. Since the initial state itself seems to be more physical and more practical in comparison with the unitary transformation, hereafter we focus on formula (23).…”

“…Moreover, been achieved for a model system (such as the nearest neighbor XY Hamiltonian in [2][3][4]), it becomes destroyed by imperfections, such as remote node interactions and quantum noise, which always reduce the state transfer fidelity [8,[10][11][12][13] so that the original state can not be perfectly transfered between the ends of a chain. As a consequence, the high-fidelity/probability state transfer becomes more popular in comparison with the PST, which is justified in numerous papers concerning different aspects of this subject, such as the entanglement [14][15][16][17][18] transfer through a quantum chain [19][20][21][22][23], the entanglement creation between distant qubits [24,25], the so-called ballistic quantum state transfer [26], the high-dimensional state transfer [27,28], the robustness of state transfer [10][11][12][13]29].…”

Temperature-dependent remote control of polarization and coherence intensity with sender’s pure initial state

“…The second one is the selective choice of the active modes (i.e., only a few of the above mentioned oscillating functions have large amplitudes, therewith their frequencies are not rational numbers) realizing the state transfer [5,6,11,13]. Both these effects are used (either explicitly or implicitly) in many contemporary state transfer algorithms [23][24][25].…”