High-fidelity quantum gates for OAM single qudits on quantum memory

The application of high-dimensional quantum systems (qudits) in quantum computing and communications seems to be a promising avenue due to the possibility of increasing the amount of information encoded in one physical carrier. In this work, we propose a method for implementing single-qudit gates for qudits based on light modes with orbital angular momentum (OAM). Method for logical qudits encoding, which ensures the quasi-cyclicity of operations, is introduced. Based on the protocol for converting the OAM of light in the Raman quantum memory scheme (Vashukevich et al 2020 Phys. Rev. A 101 033830), we show that the considered gates provide an extremely high level of fidelity of single-qudit transformations. We also compare quantum gates’ properties for systems of different dimensions and find the optimal conditions for carrying out transformations in the protocol under consideration.

Controlled cyclic remote state preparation of single-qutrit equatorial states

The scheme for controlled unidirectional cyclic remote state preparation of single-qutrit equatorial states is put forward. Alice, Bob, Charlie, and David share a seven-qutrit entangled state as the quantum channel. Under the control of David, Alice can remotely prepare a single-qutrit equatorial state at Bob’s site, Bob can remotely prepare a single-qutrit equatorial state at Charlie’s site, Charlie can remotely prepare a single-qutrit equatorial state at Alice’s site simultaneously. The direction of controlled unidirectional cyclic remote state preparation can be reversed by changing measured qutrits of the quantum channel. The scheme for controlled bidirectional cyclic remote state preparation of single-qutrit equatorial states is also proposed. The schemes can be generalized to controlled unidirectional and bidirectional multi-party cyclic remote state preparation of single-qudit equatorial states.

Malevich’s Suprematist Composition Picture for Spin States

This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the planar picture of quantum states, using the elementary geometry. The approach is based on, so called, Malevich square representation of the single qubit state. It is shown that the quantum statistics of the single qudit with some spin j and observables are formally equivalent to statistics of the classical system with N 2 - 1 random vector variables and N 2 - 1 classical probability distributions, obeying special constrains, found in this study. We present a universal inequality, that describes the single qudits state quantumness. The inequality provides a possibility to experimentally check up entanglement of the system in terms of the classical probabilities. The simulation study for the single qutrit and ququad systems, using the Metropolis Monte-Carlo method, is obtained. The geometrical representation of the single qudit states, presented in the paper, is useful in providing a visualization of quantum states and illustrating their difference from the classical ones.

Anomalous Decay and Decoherence in Atomic Gases

Pair collisions in atomic gases lead to decoherence and decay. Assuming that all the atoms in the gas are equally likely to collide one is led to consider Lindbladian of mean field type where the evolution in the limit of many atoms reduces to a single qudit Lindbladian with quadratic nonlinearity. We describe three smoking guns for nonlinear evolutions: power law decay and dephasing rates; dephasing rates that take a continuous range of values depending on the initial data and finally, anomalous flow of the Bloch ball towards a hemisphere.