Generalized Quantum Two-Qutrit-State Splitting

Jun Liu, Yimin Liu, Zhanjun Zhang

Zhang Wen, Kuangwei Xiong, Zuo Xue-Qin +1 more

In this paper we propose two quantum information splitting (QIS) schemes respectively for splitting an unknown single-qutrit and single-ququart state via three pairs of two-qubit partially entangled state. The necessary measurements and operations are given detailedly and the success probabilities are worked out. The two schemes can be directly generalized to QIS of multi-qutrit and multi-ququart states by using Bell-states channel.

Yuan Hao, Yimin Liu, Zhanjun Zhang

A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed, where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties. With the sender's help, if and only if both receivers collaborate together, they can securely share the quantum state in a probabilistic way by introducing an ancilla qutrit and performing appropriate unitary operations. The relation between the success probability and coefficients characterizing the quantum channel is revealed. The security of the present scheme is analyzed and confirmed. Moreover, the generalization of the three-party scheme to more-party case is also sketched.

Tushti Patel, V. S. Prasannaa

We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its implementation. We design Weyl-Heisenberg gadgets, the qutrit equivalents of Pauli gadgets, and come up with a practical implementation scheme for qutrit HHL. We test HHL with qutrits for simple matrices and verify the results against the expected outcomes. We apply the algorithm to quantum chemistry, and in particular, to the potential energy curve calculations of the model problem of the Hydrogen molecule in the split valence basis. We do so for two cases: 1-qutrit and 2-qutrit input states, where the latter makes use of our gadgets. We compare the number of qudits and the number of gates required between qubit and qutrit HHL implementations. In general, we find that for a fixed precision, the qutrit HHL circuit requires fewer number of qudits and comparable number of two-qudit gates than its qubit counterpart.

Yuan Hao, Yimin Liu, Lian-Fang Han +1 more

A tripartite scheme for securely sharing an arbitrary unknown two-qutrit state is proposed, where two generalized Greenberger–Horne–Zeilinger (GHZ) states serve as the quantum channel linking the three legitimate parties. The quantum information (i.e., the arbitrary unknown two-qutrit state) from the sender can be split in such a way that it can be reconstructed deterministically by any agent via a proper unitary operation provided that both agents collaborates together. Moreover, the generalization of the tripartite scheme to more-party case is also outlined.