We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.

quant-pharXiv:2609.17498Sep 16, 20260 citations

Probabilistic coding of quantum states

Andrzej Grudka, Antoni Wójcik, Mikołaj Czechlewski

We discuss the properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preserves the entanglement between the qubits to be encoded and the environment and can also be applied to mixed states. We present a protocol that enables encoding of $n$ qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of $k$ qudits. We give a formula for the probability of successful decoding.We discuss the properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preserves the entanglement between the qubits to be encoded and the environment and can also be applied to mixed states. We present a protocol that enables encoding of $n$ qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of $k$ qudits. We give a formula for the probability of successful decoding.

arXiv:quant-ph/0603244Physical Review AJul 6, 20062 citations

Encoding and measuring information in high-dimensional quantum states

Mahdi Qaryan

Jul 6, 20220 citations

Controlled Probabilistic Teleportation of Three-dimension Cat-like State

Shi Jin

Two schemes for controlled probabilistic teleportation of three-particle three-dimension cat-like state are proposed.In the first scheme,a partial five-particle qutrit entangled state is used as the quantum channel,while in the second scheme,two partial two-particle qutrit entangled states and a partial entangled three-particle qutrit state are used as the quantum channel.The classical communication cost required in both schemes is difference.The successful probability of the two schemes is difference either.Two schemes for controlled probabilistic teleportation of three-particle three-dimension cat-like state are proposed.In the first scheme,a partial five-particle qutrit entangled state is used as the quantum channel,while in the second scheme,two partial two-particle qutrit entangled states and a partial entangled three-particle qutrit state are used as the quantum channel.The classical communication cost required in both schemes is difference.The successful probability of the two schemes is difference either.

Acta Sinica Quantum OpticaJan 1, 20090 citations

Probabilistic representation of quantum dynamics

Zbigniew Haba

Physics Letters AApr 1, 199313 citations

n

qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of

k

qudits. We give a formula for the probability of successful decoding.