Transfer of scaled multiple-quantum coherence matrices

Abstract

Multiple quantum (MQ) NMR coherence spectra, which can be obtained experimentally in MQ NMR, can be transferred from the sender to the remote receiver without mixing the MQ-coherences of different orders and distortions. The only effect of such transfer is scaling of the certain blocks of sender's density matrix (matrices of MQ-coherences of different order). Such a block-scaled transfer is an alternative to the perfect state transfer. In particular, equal scaling of higher order MQ-coherences matrices is possible. Moreover, there are states which can be transferred to the receiver preserving their zero-order coherence matrix. The examples of block-scaled transfer in spin-1/2 communication lines of 6 and 42 nodes with two-qubit sender and receiver are presented.PACS numbers:

Partial structural restoring of two-qubit transferred state

“…To better characterize the structure of the unitary transformation, we pass to the scalar indexes from the Dirac notations (8) through the rule (n 1 n 2 n 3 n 4 ) (0000) (0001) (0010) (0011) (0100) (0101) (0110) (1000) (1001) (1010) (1100) i 1 2 3 4 5 6 7 8 9 10 11 (21) and write the basis of the Lie algebra associated with this unitary transformation. This basis consists of 42 non-diagonal elements γ (1;ij) , γ (2;ij) , j > i (diagonal elements are not useful in our transformations) with the following non-zero elements:…”

“…In this paper we modify the mentioned protocol by implementing the extended receiver (the subsystem at the receiver side embedding the receiver itself [21]) and the fixed optimizing unitary transformation on it. We emphasize that, being fixed, the optimizing unitary transformation represents a part of the protocol and remains the same for any transferred state.…”

Transfer of 0-order coherence matrix along spin-1/2 chain

“…Recently the concept of transfer of non-interacting multi-quantum coherence matrix was introduced [9]. Then, it was pointed in [10] that the zero-order coherence matrix of special form can be perfectly transferred from the sender to the receiver along the tripartite spin system (which includes sender S, transmission line T L, and receiver R) with the only requirements that the Hamiltonian is conserving the excitation number of the spin system and, in addition, the initial state of T L ∪ R must be a 0-order coherence matrix (it is a thermodynamic equilibrium state in [10]). Notice that the unitary transformation of the extended receiver was not used in [10].…”

“…Then, it was pointed in [10] that the zero-order coherence matrix of special form can be perfectly transferred from the sender to the receiver along the tripartite spin system (which includes sender S, transmission line T L, and receiver R) with the only requirements that the Hamiltonian is conserving the excitation number of the spin system and, in addition, the initial state of T L ∪ R must be a 0-order coherence matrix (it is a thermodynamic equilibrium state in [10]). Notice that the unitary transformation of the extended receiver was not used in [10]. Next, in [11], general statements regarding the perfect transfer of a 0-order coherence matrix were formulated for the case of the ground initial state of the subsystem T L ∪ R. In that case, an additional unitary transformation should be applied to the final receiver's state which exchanges two elements of the receiver density matrix: the elements corresponding to 0-and maximal excitation number.…”

“…Continuing the results of Refs. [9][10][11][12], the concept of optimal state transfer was formulated. This optimal state transfer is the structural restoring of the higher order coherence matrices of the initial sender's state and perfect transfer of the 0-order coherence matrix, or, if desired, the structural restoring of the whole nondiagonal part of the receiver's initial state and perfect transfer of its diagonal part.…”