Narrow Results

We briefly trace the progress in study of Bell–CH inequalities from two-level systems to its higher dimensional versions. We also present a Bell–CH and CHSH-like inequality for three-dimensional systems.

In this paper, we introduce a scheme of bidirectional quantum controlled teleportation for exchanging two single-qudit states via partially entangled GHZ-type states. The necessary measurements and operations are given in detail.

We investigate the mutual information and entanglement of stationary states of two locally driven qubits under the influence of collective dephasing. It is shown that both the mutual information and the entanglement of two qubits in the stationary state exhibit damped oscillation with the scaled action time γT of the local external driving field. It means that we can control both the entanglement and total correlation of the stationary state of two qubits by adjusting the action time of the driving field. We also consider the influence of collective dephasing on the entanglement of two qutrits and obtain the sufficient condition that the stationary state is entangled.

Quantum computation relies on exploiting quantum mechanical phenomena, and has received significant attention in recent years. Higher-dimensional quantum systems increase the density of encoded information per computing element (e.g., qutrit for three-level system), resulting in less resource overhead. For instance, 63% reduction in the number of qutrits is possible for ternary quantum systems as compared to the corresponding binary systems. The proposed work exploits this fact to synthesize ternary reversible circuits employing a cycle-based technique. The method starts from the ternary reversible specification of a given function in the form of a permutation. The permutation cycles are factored into simpler three-cycles and two-cycles, which are then mapped to ternary reversible gates. Different gate libraries are used to synthesize three-cycles and two-cycles, respectively. A gate decomposition approach is also proposed to synthesize a quantum gate netlist in terms of elementary ternary quantum gates, viz. Muthukrishnan–Stroud gate and shift gate. Synthesis results on benchmark functions indicate that the proposed method results in 27% and 6% improvements in quantum cost and gate count, respectively, over existing works in the literature.

In this paper we show a Clauser-Horne (CH) inequality for two three-level quantum systems or qutrits, alternative to the CH inequality given by Kaszlikowski et al. [Phys. Rev. A65, 032118 (2002)]. In contrast to this latter CH inequality, the new one is shown to be equivalent to the Clauser-Horne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the strongest resistance to noise for a nonmaximally entangled state for the case of two von Neumann measurements per site, as first shown by Acin et al. [Phys. Rev. A65, 052325 (2002)]. This equivalence, however, breaks down when one takes into account the less-than-perfect quantum efficiency of detectors. Indeed, for the noiseless case, the threshold quantum efficiency above which there is no local and realistic description of the experiment for the optimal choice of measurements is found to be for the CH inequality, whereas it is equal to for the CHSH inequality.

Quantum entanglement, like other resources, is now considered to be a resource. It can be produced, concentrated if required, swapped, transported and consumed. During recent years, various schemes of quantum state teleportation have been proposed using different types of quantum channels. Not restricting to qubit based systems, qutrit states and channels have also been of considerable interest. In the present paper, we investigate the teleportation of an unknown single qutrit state, as well as a two qutrit state through a three qutrit quantum channel, along with the required operations to recover the state. This is further generalized to the case of teleportation of an n-qutrit system.

The transfer of entanglement from source particles (SPs) to target particles (TPs) via the Heisenberg interaction H = s₁ ⋅ s₂ has been investigated. In our research, TPs are two qubits and SPs are two qubits or qutrits. When TPs are two qubits, we find that no matter what state the TPs are initially prepared in, at the specific time t = π the quantity of entanglement of the TPs can attain 1 after interaction with the SPs which stay on the maximally entangled state. When TPs are two qutrits, the maximal quantity of entanglement of the TPs is proportional to the quantity of entanglement of the initial state of the TPs and cannot attain 1 for almost all the initial states of the TPs. Here we propose an iterated operation which can make the TPs go to the maximal entangled state.

We study qutrit teleportation and its fidelity in the presence and absence of intrinsic decoherence through a qutrit channel. The channel consists of a Heisenberg chain with $xyz$ interaction model and the intrinsic decoherence is implemented through the Milburn model. It is shown that while the fidelity diminishes due to intrinsic decoherence, it may be enhanced if the channel is initially in an entangled state. It is also observed that, for stronger intrinsic decoherence, the initial entanglement of the channel is more effective in enhancing of fidelity.

We investigate the dynamics of entanglement, quantum discord (QD) and state coherence in a bipartite and noninteracting spin-qutrits system under mixed classical noises. Specifically, the collective effects of static noise (SN) and random telegraphic noise (RTN) each being coupled with a marginal system, are analyzed. While the static noise models a non-Markovian environment, the dynamic noise can model both a Markovian or a non-Markovian environment, and both dynamics are studied. We show that quantum correlations and coherence may survive the noise degrading effects at sufficiently long time when the Markovian regime of the RTN is considered. Meanwhile, the opposite is found in the non-Markovian regime, wherein the nonmonotonic dynamics of quantum features avoid sudden death phenomena. However, the static noise is more fatal to the survival of quantum correlations and quantum state coherence as compared to the RTN.

Measurement-Device-Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We compare the database security and client’s privacy in MDI QPQ for qubits with qutrits. For some instances, we observe that qutrit will provide better security for database than qubit. However, when it comes to the question of client’s privacy, we have to take additional measures in case of qutrit. Hence, we conclude that though in case of Quantum Key Distribution (QKD) higher dimension provides better security, in case of QPQ this is not obvious.

The classical and quantum correlations for a family of two-qutrit states are investigated. For this purpose, a family of two-qutrit states, as well as a set of measurements are proposed. An analytical quantum discord treatment is presented for this family of two-qutrit states. Finally, we compute and illustrate the entanglement of formation, classical mutual information and quantum discord for this family of two-qutrit quantum states.

For a three-level system monitored by an ancilla, we show that the quantum Zeno effect can be employed to control quantum jump for error correction. Further, we show that we can realize cNOT gate, and effect dense coding and teleportation using a three-level system with an ancilla. We believe that this work paves the way to generalize the control of a qudit.

We present an analysis of spontaneous emission in a 3-level atom as an example of a qutrit state under the action of noisy quantum channels. We choose a 3-level atom with V–configuration to be the qutrit state. Gell-Mann matrices and a generalized Bloch vector (8-dimensional) are used to describe the qutrit density operator. Using the time-evolution equations of atomic variables we find the Kraus representation of spontaneous emission quantum channel (SE channel). Furthermore, we consider a generalized Werner state of two qutrits and investigate the separability condition. We give similar analysis of spontaneous emission for qubit channels. The influence of spontaneous emission on the separability of Werner states for qutrit and qubit states is compared.