[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86176-en":3,"doc-seo-86176-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86176,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Distributed Semantics for Distributed Quantum Computing","A quantum process calculus is presented to split system state along process boundaries and evolve each process in isolation without losing information about the joint state, formalized as spatial compositionality. Existing quantum process calculi rely on global state vectors or density matrices, preventing lossless splitting due to entanglement. The work models qubit states using Deutsch–Hayden descriptors, enabling arbitrary splitting/merging of qubit stores and giving qubit transfer messages the actual state. It defines process equivalence, proves a bisimulation with soundness simplified by compositionality, and models open entanglement, illustrated on BB84 key distribution.","arXiv :2607 . 11216v1 [ quant-ph] 13 Jul 2026  \nDistributed Semantics for Distributed Quantum Computing  \nJUN INOUE, National Institute of Advanced Industrial Science and Technology, Japan  \nWe present a quantum process calculus that can split the system state along process boundaries and follow the evolution of each process in isolation, without losing information about the joint state—a property we call spatial compositionality. Compositionality is the key to reasoning about any complex system, yet quantum process calculi have struggled to provide its spatial kind, which would enable analyzing a system one process at a time. Many a quantum process calculi have been proposed, but they invariably rely on a global state representation based on state vectors or density matrices, with no known way to split them without losing information about entanglement.  \nWe propose to model quantum states with Deutsch-Hayden descriptors instead, which provide a modular representation of qubit states and their evolution. We adapt these descriptors to allow arbitrary splitting and merging of the store of qubits, leading to an unusual process calculus in which qubit transfer messages carry the actual state of the qubit, where existing calculi transfer only a reference. The calculus gives localized views of system state visible to each process, which can be assembled back together into the joint state. We define a notion of process equivalence with extensive justification grounded in physics and show a bisimulation whose soundness proof is simplified by spatial compositionality. The calculus can model open systems entangled with external processes, and we demonstrate this capability on a fragment of the BB84 key distribution protocol. This exercise shows that Deutsch-Hayden descriptors can successfully track qubit movements across process and system boundaries, though it needs help from density matrices to reason about information flow.  \nCCS Concepts: • Theory of computation → Quantum information theory; Process calculi; • Software and its engineering → Semantics; Software verification; • Networks → Formal specifications.  \nAdditional Key Words and Phrases: Quantum Communication, Quantum State Representation, Process Compositionality  \n1 Introduction  \nIn this article, we present a quantum process calculus whose semantics can follow the evolution of each process in isolation, in such a way that the results can be uniquely assembled back into the evolved joint system state, regardless of entanglement. We call this property spatial compositionality.  \nAn important application of quantum computation is in communication protocols, such as cryptographic key distribution. These protocols are distributed quantum algorithms, which have a natural home in quantum process calculi. A number of process calculi have been proposed against this backdrop, such as QPAlg [15], CQP [11], qCCS [9], and lqCCS [6] .  \nAll of these calculi lump the quantum states held by all processes into a single, monolithic state. Formally, they define a labeled transition system whose nodes are configurations that look like ⟨􀀥, 􀁤⟩ (plus bookkeeping data), where 􀁤 is a state vector or density matrix spanning not just the qubits held by process 􀀥 but all other processes that may be running in parallel. But those representations are not modular, giving no lossless way to split the system state into process-local views. Partial trace, the only generally accepted tool for narrowing the view of a density matrix, produces local views that collectively cannot recover the global state—it loses information.  \nWrit large, a monolithic semantics cannot model fully open system that interact and entangle with the outside world. For example, qCCS has a construct for external input, but it requires that the incoming qubit is unentangled with the local ones. Writ small, a monolithic semantics cannot analyze the system’s processes individually, because the effects of operation in one process ripple","cbCaij3hZ0QE6iBT","https://ap.wps.com/l/cbCaij3hZ0QE6iBT","pdf",632455,5,1,27,"English","en",105,"# Introduction\n# Jun Inoue\n## Modular reasoning and spatial compositionality\n## Deutsch–Hayden descriptors and lossless reconstruction\n## Contributions overview","[{\"question\":\"What problem does the proposed calculus address in distributed quantum computing?\",\"answer\":\"It targets the lack of a spatially compositional reasoning framework in quantum process calculi, where global state representations make it impossible to split system state into process-local views without losing information about entanglement.\"},{\"question\":\"How are Deutsch–Hayden descriptors used to enable lossless splitting?\",\"answer\":\"Quantum states are represented with Deutsch–Hayden descriptors that track modifications locally to each qubit. Unlike partial traces, the individual descriptors can be assembled to reconstruct the joint system state, even when qubits are entangled.\"},{\"question\":\"What do qubit transfer messages carry in the new process calculus?\",\"answer\":\"They carry the actual state of the qubit, whereas existing calculi typically transfer only a reference.\"}]",1784209129,68,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"distributed-semantics-for-distributed-quantum-computing","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/distributed-semantics-for-distributed-quantum-computing/86176/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the proposed calculus address in distributed quantum computing?","Question",{"text":76,"@type":77},"It targets the lack of a spatially compositional reasoning framework in quantum process calculi, where global state representations make it impossible to split system state into process-local views without losing information about entanglement.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How are Deutsch–Hayden descriptors used to enable lossless splitting?",{"text":81,"@type":77},"Quantum states are represented with Deutsch–Hayden descriptors that track modifications locally to each qubit. Unlike partial traces, the individual descriptors can be assembled to reconstruct the joint system state, even when qubits are entangled.",{"name":83,"@type":74,"acceptedAnswer":84},"What do qubit transfer messages carry in the new process calculus?",{"text":85,"@type":77},"They carry the actual state of the qubit, whereas existing calculi typically transfer only a reference.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":20,"slug":138},19,"General","general"]