On the properties of qudits

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini +1 more

Arash Pourkia

We construct solutions of the Yang–Baxter equation in any dimension $$d\ge 2$$ by directly generalizing the previously found solutions for $$d=2$$ . We equip those solutions with unitarity and entangling properties. Being unitary, they can be turned into $$2$$ -qudit quantum logic gates for qudit-based systems. The entangling property enables each of those solutions, together with all $$1$$ -qudit gates, to form a universal set of quantum logic gates.

Julio Guerrero, Antonio Sojo, Alberto Mayorgas +1 more

Abstract In this paper we study the entanglement in symmetric N-quDit systems. In particular we use generalizations to U(D) of spin U(2) coherent states (CSs) and their projections on definite parity c ∈ Z 2 D − 1 (multicomponent Schrödinger cat) states and we analyse their reduced density matrices when tracing out M < N quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to prove a theorem for the decomposition of a N-quDit Schrödinger cat state with a given parity c into a sum over all possible parities of tensor products of Schrödinger cat states of N − M and M particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ( N , M → ∞ , M / N fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted CSs of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

Tomasz Paterek

S. Balakrishnan

It is known that SWAP operation for quantum systems of arbitrary dimension can be implemented using various qudit gates. In this paper, equivalence of some important qudit operations is demonstrated. Equivalence of the qudit operations is exploited to minimize the circuit complexity in the previously proposed qudit SWAP gate constructions. Further, constructions of qudit SWAP operation with minimum number of qudit gates are also proposed. Importantly, these circuit constructions of SWAP retain its properties like symmetry and simplicity.

Jesni Shamsul Shaari, Mohamed Ridza Wahiddin, Stefano Mancini