Two Operational Principles Single Out Quantum Theory

• URL: http://arxiv.org/abs/2605.23217v1
• Date: Fri, 22 May 2026 04:19:55 GMT
• Title: Two Operational Principles Single Out Quantum Theory
• Abstract summary: Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs)<n>We prove that two postulates suffice: local input-output statistics identify channels, and every state admits an equivalent-system purification, unique up to reversible dynamics.<n>The full complex quantum formalism follows; every consistent probability rule is realized as a POVM, so measurement no-restriction is derived rather than assumed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates suffice: local input-output statistics identify channels, and every state admits an equivalent-system purification, unique up to reversible dynamics. The full complex quantum formalism follows; every consistent probability rule is realized as a POVM, so measurement no-restriction is derived rather than assumed.

Related papers

• The composition rule for quantum systems is not the only possible one [0.0]
  We argue that the composition postulate deserves to be experimentally scrutinised independently of the other features of quantum theory.<n>We formulate a family of operational theories that are solely distinguished from standard quantum theory by their system-composition rule.
  arXiv  Detail & Related papers  (2024-11-24T19:31:13Z)
• Absolute dimensionality of quantum ensembles [41.94295877935867]
  The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis.<n>We propose an absolute, i.e.basis-independent, notion of dimensionality for ensembles of quantum states.
  arXiv  Detail & Related papers  (2024-09-03T09:54:15Z)
• Probabilistic Unitary Formulation of Open Quantum System Dynamics [1.8416014644193066]
  We show that all non-relativistic quantum processes, whether open or closed, are unitary or probabilistic unitary.<n>For open quantum systems, its continuous dynamics can always be described by the Lindblad master equation with all jump operators being unitary.<n>This formalism is shown to be exact under all cases, and does not rely on any assumptions other than the continuity and differentiability of the density matrix.
  arXiv  Detail & Related papers  (2023-07-11T20:07:03Z)
• Second Response Theory: A Theoretical Formalism for the Propagation of Quantum Superpositions [0.0]
  We expand a previously developed size-extensive formalism within coupled cluster theory, called second response theory, so it propagates quantum systems. Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences.
  arXiv  Detail & Related papers  (2023-06-13T17:33:22Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Perturbation Theory for Quantum Information [1.2792576041526287]
  We develop theories for two classes of quantum state perturbations, perturbations that preserve the vector support of the original state and perturbations that extend the support beyond the original state. We apply our perturbation theories to find simple expressions for four of the most important quantities in quantum information theory.
  arXiv  Detail & Related papers  (2021-06-10T06:49:41Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality [0.6882042556551611]
  We study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors. We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures. We report a relation between quantum coherence and path complementary distinguishability in a double-slit set-up.
  arXiv  Detail & Related papers  (2020-05-17T16:56:31Z)

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.