Pure State Transformations under Block Coherence

• URL: http://arxiv.org/abs/2605.30588v1
• Date: Thu, 28 May 2026 21:35:02 GMT
• Title: Pure State Transformations under Block Coherence
• Abstract summary: Block coherence provides a natural generalization of standard quantum coherence by treating superpositions across different subspaces as a resource.<n>This work studies deterministic pure-state conversion under three free operations: physically block incoherent operations (PBIO), strictly block incoherent operations (SBIO), and block dephasing covariant incoherent operations (BDCO)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Block coherence provides a natural generalization of standard quantum coherence by treating superpositions across different subspaces as a resource. This work studies deterministic pure-state conversion under three free operations: physically block incoherent operations (PBIO), strictly block incoherent operations (SBIO), and block dephasing covariant incoherent operations (BDCO). For PBIO, we prove that, under a natural nondegeneracy condition on the active Kraus branches, any deterministic conversion from one pure state to another must be implemented by a block incoherent unitary. When the nondegeneracy requirement is removed, the condition becomes more general. It demands that the blockwise action of every active branch reproduce the target block structure with a common proportionality factor across all output blocks. For SBIO and BDCO, we show that deterministic pure-state transformation is completely characterized by the majorization relation between the input and output block probability vectors. The converse proof is constructive, yielding an explicit Kraus representation for every admissible BDCO transformation. In the rank-one limit, these conditions reduce to the known pure-state transformation criteria for physically incoherent operations (PIO), strictly incoherent operations (SIO), and dephasing covariant incoherent operations (DIO) in the standard resource theory of coherence. Using the majorization condition, a maximally block-coherent state with uniform block weights is also identified as a universal pure-state resource under BDCO and SBIO. We have also provided geometric numerical illustrations comparing the state transformation power of BDCO and DIO for a fixed input state, fixed output state and mutual convertibility scenarios.

Related papers

• Frame-Dependent Traces and the Third-Particle Paradox [45.88028371034407]
  We show that the Paradox of the Third Particle arises when comparing subsystem descriptions across Quantum Reference Tracing perspectives.<n>We argue that our condition captures the Paradox content: rather than imposing consistency on the whole state space, we reproduce exactly the states on which it holds.
  arXiv  Detail & Related papers  (2026-07-23T18:00:01Z)
• Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions [45.88028371034407]
  Block encoding provides the standard method for accessing matrix data within quantum circuits.<n>We present a unified framework for efficiently block encoding finite-difference discretizations of the Laplacian.
  arXiv  Detail & Related papers  (2026-03-12T19:35:16Z)
• Explicit C*-algebraic Protocol for Exact Universal Embezzlement of Entanglement [7.410574751379865]
  We present an explicit construction of a universal embezzlement protocol in the C*-algebraic model of quantum information.<n>Our approach is both exact and state-independent.<n>This offers a conceptually intuitive model for universal entanglement embezzlement in infinite-dimensional settings.
  arXiv  Detail & Related papers  (2025-06-12T14:26:11Z)
• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• State convertibility under genuinely incoherent operations [0.0]
  State convertibility is fundamental in the study of resource theory of quantum coherence. In this paper, we give a complete characterization of state convertibility under genuinely incoherent operations.
  arXiv  Detail & Related papers  (2024-08-06T01:28:53Z)
• On convertibility among bipartite 2x2 entangled states [0.8702432681310401]
  It is impossible to convert to an entangled state with lower rank under separable operations. It is conjectured that MEMS may lie on the bottom of entangled state ordering for given entanglement of formation.
  arXiv  Detail & Related papers  (2024-02-13T01:53:48Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Quantum coherence between subspaces: State transformation, Cohering Power, $k$-coherence and other properties [0.0]
  We develop a framework which facilitates further investigation of bock-coherence. We define the concept of block-cohering and block-decohering powers of quantum channels. We explore the relation between block coherence and a previous extension of coherence, known as $k$-coherence.
  arXiv  Detail & Related papers  (2023-02-25T20:09:59Z)
• Real quantum operations and state transformations [44.99833362998488]
  Resource theory of imaginarity provides a useful framework to understand the role of complex numbers. In the first part of this article, we study the properties of real'' (quantum) operations in single-party and bipartite settings. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations.
  arXiv  Detail & Related papers  (2022-10-28T01:08:16Z)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• 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)
• Discrimination of quantum states under locality constraints in the many-copy setting [18.79968161594709]
  We prove that the optimal average error probability always decays exponentially in the number of copies. We show an infinite separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB) On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB.
  arXiv  Detail & Related papers  (2020-11-25T23:26:33Z)
• Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
  Universal quantum computing with continuous variables requires non-Gaussian resources. The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive. We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
  arXiv  Detail & Related papers  (2020-07-07T09:19:49Z)

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.