Polish physicists construct entangled states with prime power dimensions

New Families of Absolutely Maximally Entangled States

Polish physicists from the Polish Academy of Sciences have presented a constructive method for generating absolutely maximally entangled (AME) states in systems whose local dimension is twice a prime‑power. Their work shows that AME(13, 2q) states exist for any prime power q ≥ 17, and more generally that AME(N, 2q) states can be built for odd N ≥ 3 provided the dimension q meets a simple exponential bound.

How the Construction Works

The authors combine qubit registers with higher‑dimensional q‑level systems. By superposing products of qubit and q‑level states, interference between different branches of the overall wavefunction is cancelled, allowing the qubits to achieve maximally mixed reductions only on average. A “parent” AME state is first projected to remove one party, then paired with a carefully chosen qubit mixture. This coupling yields new AME states without requiring full entanglement across every subset of parties.

Concrete Results and Thresholds

• AME(13, 2q) is achievable for any prime power q ≥ 17.
• AME(15, 2q) can be built when q ≥ 9, and a cyclic‑shift construction produces AME(15, 2p) for every prime p.
• AME(17, 2q) requires q ≥ 67.
• For nine parties the authors complete the classification: an AME(9, d) state exists iff d ≥ 3.

These families are infinite; the required local dimension q grows exponentially with the number of parties, reflecting a fundamental scaling limitation.

Significance for Quantum Information

AME states are a benchmark of multipartite entanglement and have applications in quantum error‑correcting codes, secret sharing, and holographic tensor‑network models. Providing explicit, verifiable constructions moves the field beyond existence proofs and offers concrete test cases for experimental platforms that can host higher‑dimensional quantum systems (e.g., trapped ions, neutral atoms, or photonic qudits).

Outlook

The authors make their code and detailed proofs publicly available, enabling independent verification and further extensions. Future work will likely explore whether the coupling technique can be adapted to physical architectures and whether the exponential growth of q can be mitigated through alternative constructions or hybrid error‑correction schemes.

--- The findings are described in the pre‑print arXiv:2611.17216v1.