Maximal complementarity in the n-qubit Pauli group

• URL: http://arxiv.org/abs/2607.24988v1
• Date: Mon, 27 Jul 2026 18:40:40 GMT
• Title: Maximal complementarity in the n-qubit Pauli group
• Abstract summary: Maximal sets of non-degenerate complementary observables are known to exist in systems of prime power dimension such as n-qubit systems.<n>We prove that observables associated with the n-qubit Pauli group also exhibit complementarity under this restriction.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Observables in quantum mechanics are generally complementary, that is, they reveal mutually incompatible pieces of information about a given system. This property is not only a fundamental tenet of the quantum formalism, but also a key component in quantum cryptographic protocols. As such it has fuelled much research into finding sets of highly complementary observables. In its strongest form -- the one we consider in this work -- the information between complementary observables is not merely incompatible but mutually exclusive: maximal information about one observable implies no information about the other, and vice versa. Maximal sets of non-degenerate complementary observables are known to exist in systems of prime power dimension such as n-qubit systems. Here, we study complementarity of degenerate observables, specifically we prove that observables associated with the n-qubit Pauli group also exhibit complementarity under this restriction: first, we obtain a criterion for two such observables to be complementary and, second, we relate maximal sets of complementary observables with informational pure state complementarity equalities, further studied in two companion papers. Equivalently, these results can be formulated in terms of maximal complementary sets of (not necessarily maximal) Abelian subgroups of the Pauli group linking with (possibly coarse-grained) mutually unbiased bases. Finally, we prove that these complementarity sets entail strong entropic uncertainty relations.

Related papers

• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• No Absolute Hierarchy of Quantum Complementarity [0.0]
  Bohr's principle of complementarity prohibits simultaneous access to certain physical properties within a single experimental arrangement.<n>We show that this hierarchy ceases to be absolute in the multi-copy regime.<n>We uncover a configuration-dependent structure of complementarity, reveal a subtle role of entanglement in shaping the structure of measurement limitations.
  arXiv  Detail & Related papers  (2026-02-26T09:29:00Z)
• Quantum complementarity [41.99844472131922]
  Two properties of a system are considered complementary if they cannot be simultaneously well defined.<n>In quantum theory, this notion is equivalent to the incompatibility of operations -- that is, their inability to be performed simultaneously.
  arXiv  Detail & Related papers  (2025-10-12T20:37:06Z)
• Precision bounds for multiple currents in open quantum systems [37.69303106863453]
  We derivation quantum TURs and KURs for multiple observables in open quantum systems undergoing Markovian dynamics.<n>Our bounds are tighter than previously derived quantum TURs and KURs for single observables.<n>We also find an intriguing quantum signature of correlations captured by the off-diagonal element of the Fisher information matrix.
  arXiv  Detail & Related papers  (2024-11-13T23:38:24Z)
• Complementarity-based complementarity: the choice of mutually unbiased observables shapes quantum uncertainty relations [0.0]
  We show that uncertainty relations can depend on the choice of observables.<n>We show that selecting different sets of three MUBs in a 5-dimensional quantum system results in distinct uncertainty bounds.
  arXiv  Detail & Related papers  (2024-06-17T10:29:53Z)
• Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables [0.0]
  We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities.
  arXiv  Detail & Related papers  (2023-09-22T08:51:34Z)
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables [0.0]
  We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system.<n>It is found that one cannot prepare a quantum state with probability vectors of incompatible observables spreading out arbitrarily.<n>We also explore the connections between quantum uncertainty and quantum coherence, and obtain a complementary relation for the quantum coherence as well.
  arXiv  Detail & Related papers  (2023-08-10T16:44:10Z)
• Incompatibility of observables, channels and instruments in information theories [68.8204255655161]
  We study the notion of compatibility for tests of an operational probabilistic theory. We show that a theory admits of incompatible tests if and only if some information cannot be extracted without disturbance.
  arXiv  Detail & Related papers  (2022-04-17T08:44:29Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Entanglement Monotones from Complementarity Relations [0.0]
  Bohr's complementarity and Schr"odinger's entanglement are prominent physical characters of quantum systems. For any complete complementarity relation involving predictability and visibility measures that satisfy the criteria established in the literature, these corresponding quantum correlations are entanglement monotones.
  arXiv  Detail & Related papers  (2020-12-28T20:08:21Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.