Using a generalization of the invariant information introduced by Brukner and Zeilinger [Phys. Rev. Lett. 83, 3354 (1999)] to high-dimensional systems, we introduce a complementarity relation between the local and nonlocal information for $d\ifmmode\times\else\texttimes\fi{}d$ systems under an isolated environment, where $d$ is prime or a power of a prime number. We also analyze the dynamics of the local information in the decoherence process.Using a generalization of the invariant information introduced by Brukner and Zeilinger [Phys. Rev. Lett. 83, 3354 (1999)] to high-dimensional systems, we introduce a complementarity relation between the local and nonlocal information for $d\ifmmode\times\else\texttimes\fi{}d$ systems under an isolated environment, where $d$ is prime or a power of a prime number. We also analyze the dynamics of the local information in the decoherence process.

arXiv:0708.4060Physical Review AJul 26, 20077 citations

Information Invariance and Quantum Probabilities

Časlav Brukner, Anton Zeilinger

arXiv:0905.0653Foundations of PhysicsMay 26, 200991 citations

An algebraically closed family of informational n-qubit purity invariants

Markus Frembs, Giovanni Natale, Christopher S. P. Wever +1 more

We present a family of quadratics in Pauli expectation values, and prove that they constitute state-independent invariants for all n-qubit pure states. This family generalises the two-qubit `pentagon identities', discovered in the reconstruction programme of [P. A. Höhn, Quantum 1, 38 (2017), P. A. Höhn and C. S. P. Wever, Phys. Rev. A 95, 012102 (2017)], where they characterise the space of pure states, as well as the unitary group, and are interpreted as complementarity equalities in the Brukner-Zeilinger information measure. The generalisation to arbitrarily many qubits is nontrivial as it requires new tools which in turn reveal novel structural properties that are absent in the two-qubit case. A thorough analysis of these properties, and their relation with mutual unbiasedness and complementarity in the n-qubit Pauli group, can be found in two companion papers.We present a family of quadratics in Pauli expectation values, and prove that they constitute state-independent invariants for all n-qubit pure states. This family generalises the two-qubit `pentagon identities', discovered in the reconstruction programme of [P. A. Höhn, Quantum 1, 38 (2017), P. A. Höhn and C. S. P. Wever, Phys. Rev. A 95, 012102 (2017)], where they characterise the space of pure states, as well as the unitary group, and are interpreted as complementarity equalities in the Brukner-Zeilinger information measure. The generalisation to arbitrarily many qubits is nontrivial as it requires new tools which in turn reveal novel structural properties that are absent in the two-qubit case. A thorough analysis of these properties, and their relation with mutual unbiasedness and complementarity in the n-qubit Pauli group, can be found in two companion papers.

quant-pharXiv:2607.24987Jul 29, 20260 citations

Complementarity in quantum systems

András Szántó

Jan 1, 20140 citations

d

is prime or a power of a prime number. We also analyze the dynamics of the local information in the decoherence process.