Complementarity Beyond Definite Causal Order

• URL: http://arxiv.org/abs/2603.27780v1
• Date: Sun, 29 Mar 2026 17:24:51 GMT
• Title: Complementarity Beyond Definite Causal Order
• Abstract summary: We show that no universal linear additive complementarity relation exists that simultaneously captures path distinguishability, spatial coherence, and coherence between causal orders.<n>Results establish that complementarity is fundamentally shaped by causal structure and cannot, in general, be fully captured at the level of reduced quantum states alone.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Wave--particle duality is a cornerstone of quantum mechanics, traditionally formulated under definite causal order. We investigate how complementarity is modified when the temporal order of operations is coherently superposed, as in the quantum switch. We show that no universal linear additive complementarity relation exists that simultaneously captures path distinguishability, spatial coherence, and coherence between causal orders. This reveals a fundamental separation between spatial and causal resources, which reside on different subsystems and are therefore not jointly constrained by a single quantum state. While tracing out the order qubit recovers the standard duality relation at the level of the reduced quanton--detector state, coherence between causal orders is not accessible at the level of the reduced description. To capture this contribution, we introduce \emph{causal coherence}, defined as the coherence of the order qubit, which quantifies interference between alternative causal orders and is operationally measurable; we construct explicit processes in which spatial duality is saturated while causal coherence is maximal. We further show that complementarity admits a state-dependent entropic formulation based on incompatible measurements on the causal degree of freedom; unlike generic state-dependent relations, this formulation arises from a universal uncertainty principle and provides a canonical operationally meaningful description. These results establish that complementarity is fundamentally shaped by causal structure and cannot, in general, be fully captured at the level of reduced quantum states alone.

Related papers

• Resource theory of coherence in continuous position basis from measurement-induced dephasing [0.0]
  We develop a resource-theoretic framework for quantum coherence directly in continuous basis.<n>We introduce a physically motivated dephasing channel based on random momentum kicks.<n>We show that continuous-basis coherence is tied to dephasing disturbance rather than to a nonempty set of diagonal states.
  arXiv  Detail & Related papers  (2026-05-09T15:53:59Z)
• Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data [45.85698554568285]
  We find necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction.<n>We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable.
  arXiv  Detail & Related papers  (2026-05-06T07:16:29Z)
• Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing [40.82628972269358]
  We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states.<n>We find that passing from simple to composite hypotheses can fundamentally change which quantum divergence determines the operational limits of discrimination.
  arXiv  Detail & Related papers  (2026-05-04T04:02:55Z)
• On Quantum Indeterminacy [0.0]
  We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge.<n>Our approach is based on convex geometry in phase space and on methods from symplectic topology.
  arXiv  Detail & Related papers  (2026-05-01T21:18:25Z)
• 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)
• Tight any-shot quantum decoupling [23.729027844524893]
  We prove a novel one-shot decoupling theorem formulated in terms of quantum entropy relative distance.<n>We show that this bound is ensemble-tight in quantum relative entropy distance.
  arXiv  Detail & Related papers  (2026-02-19T15:01:26Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• Unspeakable Coherence Concentration [0.0]
  Unspeakable coherence is a key feature separating quantum and classical physics.<n>We show that there exists states for which the ratio of the input-output coherence can be amplified unboundedly.
  arXiv  Detail & Related papers  (2025-12-03T20:46:40Z)
• Error exponents of quantum state discrimination with composite correlated hypotheses [40.82628972269358]
  We study the error exponents in quantum hypothesis testing between two sets of quantum states.<n>We introduce and compare two natural extensions of the quantum Hoeffding divergence and anti-divergence to sets of quantum states.
  arXiv  Detail & Related papers  (2025-08-18T13:04:06Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Knot invariants and indefinite causal order [0.0]
  We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number of events and spacetime configurations in superposition.<n>By constructing diagrammatic and knot-theoretic representations of the causal order between events, we find that the definiteness or maximal indefiniteness of the causal order is topologically invariant.
  arXiv  Detail & Related papers  (2024-09-17T14:36:25Z)
• Quantum Causal Inference with Extremely Light Touch [0.0]
  We give a causal inference scheme using quantum observations alone for a case with both temporal and spatial correlations.<n>The protocol determines compatibility with 5 causal structures distinguished by the direction of causal influence.
  arXiv  Detail & Related papers  (2023-03-19T02:59:05Z)
• Step-by-step derivation of the algebraic structure of quantum mechanics (or from nondisturbing to quantum correlations by connecting incompatible observables) [0.0]
  This paper provides a step-by-step derivation of the quantum formalism. It helps us to understand why this formalism is as it is.
  arXiv  Detail & Related papers  (2023-03-08T19:27:24Z)
• Entanglement as upper bounded for the nonlocality of a general two-qubit system [16.676050048472963]
  We systematically investigate the relationship between entanglement and nonlocality of a general two-qubit system. We find that the nonlocality of two different two-qubit states can be optimally stimulated by the same nonlocality test setting.
  arXiv  Detail & Related papers  (2020-04-17T16:42:27Z)

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.