Quantum Information Decoupling Beyond Finite Dimensions

• URL: http://arxiv.org/abs/2607.26123v1
• Date: Tue, 28 Jul 2026 18:00:00 GMT
• Title: Quantum Information Decoupling Beyond Finite Dimensions
• Abstract summary: We establish a framework for arbitrary separable, possibly infinite-dimensional systems.<n>For finite-dimensional inputs, we assume finite entropy of the manipulated system.<n>As an application, we construct an infinite-dimensional quantum-state-merging protocol.
• Score: 1.2691047660244335
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum information decoupling is a pillar of quantum information theory, underlying quantum communication, error correction, and information recovery. However, its existing formulations rely on random unitary operations tied to finite-dimensional assumptions on quantum systems. Here we establish a decoupling framework for arbitrary separable, possibly infinite-dimensional systems. For finite-dimensional inputs and arbitrary separable reference/output systems, we derive error bounds on one-shot decoupling for completely positive maps in terms of sandwiched Rényi conditional entropies. For partial-trace decoupling with finite-dimensional references, the error exponent is optimal up to the known critical rate. To handle infinite-dimensional inputs, we assume finite entropy of the manipulated system. We construct finite-rank projections on independent and identically distributed (IID) states to restrict randomization to a projected finite-dimensional subspace, while ensuring high success probability by including auxiliary components in the discarded subsystem at asymptotically negligible cost. This leads to an infinite-dimensional IID partial-trace decoupling protocol achieving optimal asymptotic dimension rates. As an application, we construct an infinite-dimensional quantum-state-merging protocol, a mother protocol of quantum information theory. Under finite entropy of Alice's marginal, it achieves the same quantum-communication and total-cost rates as in finite dimensions, governed by mutual information and conditional entropy. These results show that the operational interpretation of entropic quantities through these achievable rates constitutes a universal principle beyond finite dimensions. More broadly, our framework provides foundational tools for exploring quantum information regardless of whether we model the physical world using finite- or infinite-dimensional spaces.

Related papers

• State Diagnostics of Complexity in Open Quantum Systems [39.146761527401424]
  We study the emergence of complexity in finite-size quantum systems.<n>We represent mixed quantum states as probability measures on complex projective Hilbert space.
  arXiv  Detail & Related papers  (2026-08-10T15:09:52Z)
• Complexity-driven transitions in quantum observation [8.52275083968873]
  In quantum observation, destructive measurements irreversibly project quantum states into classical data.<n>We show that measurements irreversibly project quantum states into classical data.<n>By unveiling the fundamental scaling laws and transitions that govern quantum observation, our results delineate resource boundaries for quantum learning, state certification, and quantum metrology.
  arXiv  Detail & Related papers  (2026-06-08T17:27:22Z)
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases [25.094962102120178]
  We propose more stringent quantum-memory-assisted entropic uncertainty relations for complete sets of mutually unbiased bases in multipartite scenarios.<n>We present lower and upper bounds of the quantum uncertainties based on the complementarity of the observables, the purity of the measured state, the (conditional) von-Neumann entropies, the Holevo quantities and mutual information.
  arXiv  Detail & Related papers  (2026-04-05T06:23:10Z)
• 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)
• Tensor Cross Interpolation of Purities in Quantum Many-Body Systems [0.0]
  In quantum many-body systems the exponential scaling of the Hilbert space with the number of degrees of freedom renders a complete state characterization.<n>Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed.<n>In this work, we demonstrate that the entanglement feature can be efficiently defining using only a amount of samples in the number of degrees of freedom.
  arXiv  Detail & Related papers  (2025-03-21T15:33:00Z)
• 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)
• One-Shot Min-Entropy Calculation Of Classical-Quantum States And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state.<n>It offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme.<n>It gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• Entanglement cost for infinite-dimensional physical systems [6.6908747077585105]
  We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state. This generalizes a result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems.
  arXiv  Detail & Related papers  (2024-01-17T19:12:10Z)
• The signaling dimension in generalized probabilistic theories [48.99818550820575]
  The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system. We show that it suffices to consider extremal measurements with rayextremal effects, and we bound the number of elements of any such measurement in terms of the linear dimension. For systems with a finite number of extremal effects, we recast the problem of characterizing the extremal measurements with ray-extremal effects.
  arXiv  Detail & Related papers  (2023-11-22T02:09:16Z)
• Dilation theorem via Schr\"odingerisation, with applications to the quantum simulation of differential equations [29.171574903651283]
  Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. In this study, we demonstrate the viability of the recently devised Schr"odingerisation approach.
  arXiv  Detail & Related papers  (2023-09-28T08:55:43Z)
• Renormalized von Neumann entropy with application to entanglement in genuine infinite dimensional systems [0.0]
  Von Neumann quantum entropy is finite and continuous in general, infinite dimensional case. The renormalized quantum entropy is defined by the explicit use of the Fredholm determinants theory. Several features of majorization theory are preserved under then introduced renormalization as it is proved in this paper.
  arXiv  Detail & Related papers  (2022-11-10T12:56:07Z)

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.