A theoretical study suggests that a sequence of light–atom interactions could generate entangling gates between quantum systems with any chosen number of logical states. The calculation describes the resulting operation as a controlled blend of doing nothing and swapping the two systems, a structure that includes a broad family of SWAP-alpha gates.
The result comes with an important qualification: this is a model, not a laboratory demonstration. The work uses orbital-angular-momentum light interacting with collective modes in a cold four-level atomic ensemble, and reports analytical, numerical and limiting-case calculations rather than measured entanglement or a tested device.
A gate built from two interactions
The protocol, known as a QRQ sequence in the study, contains two Faraday interactions. Between them, the model rotates the quadratures of both the light and the atomic system. The strength of the interactions is set by coupling parameters, while the rotations determine how the two stages are combined.
The proposed encoding uses single excitations spread across superpositions of light modes carrying orbital angular momentum. In plain terms, the logical state is represented by which mode contains the excitation and by the superposition of those possibilities. The discreteness of these modes is what allows the model to describe logical spaces of arbitrary dimension.
Here, a qudit means a quantum system whose logical space has d possible basis states; a qubit is the special case with two. The study examines two such systems with equal dimension, one excitation in the light and one in the atomic ensemble, and asks how the modeled gate changes as d and the desired entangling power change.
To quantify entanglement, the authors use operator entangling power, a measure of how strongly a two-system operation can create entanglement. They analyze the operation with a decomposition into pairs of single-system operators and use a linear-entropy calculation, then examine the protocol numerically and through asymptotic limits.
The dimension drops out of one control problem
The calculated entangling power separates into two factors: one determined by the interaction settings and another determined by the logical dimension. That separation matters because the interaction parameters needed to produce a fixed entangling power are reported to depend only on the gate parameter alpha, not on the dimension of the logical space.
Within the modeled gate family, the protocol includes SWAP-alpha-d operations for any value of alpha. The reported maximum of the entangling-power curve occurs at alpha = (2k + 1)/2, where k is an integer. The notation describes the points in the family at which the calculated operation reaches its highest entangling power.
That flexibility does not mean every gate is equally likely to appear in the model’s desired logical subspace. The probability analysis tracks unwanted contributions from the vacuum and from excitation bunching, in which excitations collect in the same part of the system. To obtain a conservative lower bound, the calculation maximizes those contributions over the input amplitudes; the maximizing inputs have equal amplitudes and are called equal-weight states.
The resulting probabilities vary with both the interaction regime and the target gate. In the regimes examined, the case ξ1 < ξ2 has the highest asymptotic probabilities for all entangling powers. Probabilities generally fall as the requested entangling power increases and decline, almost monotonically, as the logical dimension grows; the modeled maximum occurs for two qubits.
One formal limiting result is written as d/(4d − 1) for the stated case m = 1/2. This is a theoretical asymptotic expression, not a measured success rate, and it describes a limit of the model rather than a result obtained from a finite experimental apparatus.
A further step toward a controlled gate
The paper also sketches a construction for a high-dimensional controlled-NOT, or CNOT-d, by applying the QRQ protocol twice. Its reported probability is at least 1/16 in the formal infinite-dimension limit and reaches up to 4/49 for qubits.
Those figures are estimates within the stated model. The construction also assumes that an intermediate single-qudit light transformation can be carried out deterministically with linear optical elements. The reported bounds therefore describe the proposed sequence under that assumption, rather than an experimentally established performance level.
A prediction still waiting for hardware
Nothing in the study shows experimentally generated or measured entanglement between the light and atoms. It also does not directly test the effects of optical or atomic losses, decoherence, imperfect overlap between orbital-angular-momentum modes, or errors in controlling the interaction and rotation parameters.
The probability bound is based on maximizing unwanted vacuum and bunching terms over input amplitudes, so it should not be read as the realized probability for every possible input state. Several headline results also rely on formal limiting cases involving unbounded parameters or a formally maximal logical dimension.
The authors interpret the calculations as evidence that the light–atom scheme can generate SWAP-alpha-d gates for arbitrary logical dimension and alpha while combining entanglement with quantum-memory storage. Whether those controls remain practical under experimental constraints, and whether the proposed CNOT-d sequence reaches its modeled bounds, remain open tests.
The document is an arXiv preprint, version 1, dated 20 August 2026, with no journal venue listed in the supplied record. The supplied front matter identifies Saint-Petersburg State University as the authors’ affiliation and reports no funding statement.
Paper data and sources
Original title: Entangling two qudits of arbitrary dimension through light-atomic Faraday interaction
Authors: R. Surmay, V. A. Leonov, E. A. Vashukevich
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text