Encoding and decoding are the two key steps in information processing. In this work, we study the encoding and decoding capabilities of operational theories in the context of information-storability game, where the task is to freely choose a set of states from which one state is chosen at random and by measuring the state it must be identified; a correct guess results in as many utiles as the number of states in the chosen set and an incorrect guess means a penalty of a fixed number of utiles. We connect the optimal winning strategy of the game to the amount of information that can be stored in a given theory, called the information storability of the theory, and show that one must use so-called nondegradable sets of states and nondegradable measurements whose encoding and decoding properties cannot be reduced. We demonstrate that there are theories where the perfect discrimination strategy is not the optimal one so that the introduced game can be used as an operational test for super information storability. We further develop the concept of information storability by giving new useful conditions for calculating it in specific theories.Encoding and decoding are the two key steps in information processing. In this work, we study the encoding and decoding capabilities of operational theories in the context of information-storability game, where the task is to freely choose a set of states from which one state is chosen at random and by measuring the state it must be identified; a correct guess results in as many utiles as the number of states in the chosen set and an incorrect guess means a penalty of a fixed number of utiles. We connect the optimal winning strategy of the game to the amount of information that can be stored in a given theory, called the information storability of the theory, and show that one must use so-called nondegradable sets of states and nondegradable measurements whose encoding and decoding properties cannot be reduced. We demonstrate that there are theories where the perfect discrimination strategy is not the optimal one so that the introduced game can be used as an operational test for super information storability. We further develop the concept of information storability by giving new useful conditions for calculating it in specific theories.

arXiv:2311.17522International Journal of Quantum InformationApr 30, 20240 citations

Information transfer in generalized probabilistic theories

Zhaoqi Wu, Chuanxi Zhu, Shunlong Luo +1 more

Physics Letters AAug 11, 20158 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

General probabilistic theories: An introduction

Martin Plávala

arXiv:2103.07469Physics ReportsSep 1, 202396 citations

Entropies in general probabilistic theories and their application to the Holevo bound

Gen Kimura, Junji Ishiguro, Makoto Fukui

General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this paper, we introduce a systematic method to construct a series of entropies, all of which generalize Shannon entropy in classical systems and von Neumann entropy in quantum systems. Using these entropies, the Holevo bound, an upper bound of the accessible information from a quantum system, is generalized to hold in any general probabilistic theory.General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this paper, we introduce a systematic method to construct a series of entropies, all of which generalize Shannon entropy in classical systems and von Neumann entropy in quantum systems. Using these entropies, the Holevo bound, an upper bound of the accessible information from a quantum system, is generalized to hold in any general probabilistic theory.

arXiv:1604.08009Physical Review AOct 17, 201613 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.