Mapping indefinite causal order processes to composable quantum protocols in a spacetime

• URL: http://arxiv.org/abs/2404.05319v1
• Date: Mon, 8 Apr 2024 09:09:50 GMT
• Title: Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Authors: Matthias Salzger, V. Vilasini,
• Abstract summary: We show how the formalism of quantum circuits with quantum control of causal order (QC-QC) connects with the observed composability of physical experiments in spacetime. We incorporate the set-up assumptions of the QC-QC framework into atemporal perspective and show that every QC-QC can be mapped to a causal box. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Formalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents' operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have garnered much interest. However, the interface between these information-theoretic approaches and spatiotemporal notions of causality is less understood, and questions relating to the physical realisability of ICS in a spatiotemporal context persist despite progress in their information-theoretic characterisation. Further, previous work suggests that composition of processes is not so straightforward in ICS frameworks, which raises the question of how this connects with the observed composability of physical experiments in spacetime. To address these points, we compare the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an interesting class of ICS processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC's behaviour in a relevant subspace defined by the assumptions. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC, which unravels the original ICS of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime structure. Our results also clarify how the composability of physical experiments is recovered, while highlighting the essential role of relativistic causality and the Fock space structure.

Related papers

• Strategic Code: A Unified Spatio-Temporal Framework for Quantum Error-Correction [0.0]
  Quantum error-correcting code (QECC) is the central ingredient in fault-tolerant quantum information processing. An emerging paradigm of dynamical QECC shows that one can robustly encode logical information both temporally and spatially. An overarching theory of how dynamical Qs achieve fault-tolerance is lacking.
  arXiv  Detail & Related papers  (2024-05-27T18:03:00Z)
• Quantum steering ellipsoids and quantum obesity in critical systems [0.0]
  Quantum obesity (QO) is new function used to quantify quantum correlations beyond entanglement. We show that QO is a fundamental quantity to observe signature of quantum phase transitions.
  arXiv  Detail & Related papers  (2023-12-19T19:14:08Z)
• Connecting indefinite causal order processes to composable quantum protocols in a spacetime [0.0]
  We argue that quantum circuits with quantum control of causal order (QC-QC) can be interpreted as quantum circuits with quantum controlled superpositions of orders. We show that the only class of processes that can be physically implemented in a fixed background spacetime are those that can be interpreted as quantum circuits with quantum controlled superpositions of orders.
  arXiv  Detail & Related papers  (2023-04-13T13:25:06Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• No-signalling constrains quantum computation with indefinite causal structure [45.279573215172285]
  We develop a formalism for quantum computation with indefinite causal structures. We characterize the computational structure of higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
  arXiv  Detail & Related papers  (2022-02-21T13:43:50Z)
• Quantum communication complexity beyond Bell nonlocality [87.70068711362255]
  Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks. Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. We prove that a new class of communication complexity tasks can be associated to Bell-like inequalities.
  arXiv  Detail & Related papers  (2021-06-11T18:00:09Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Quantum Simulation of Light-Front Parton Correlators [0.0]
  The physics of high-energy colliders relies on the knowledge of non-perturbative parton correlators. We propose a quantum algorithm to perform a quantum simulation of these type of correlators.
  arXiv  Detail & Related papers  (2020-11-02T19:38:33Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)
• Functorial evolution of quantum fields [0.0]
  We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata.
  arXiv  Detail & Related papers  (2020-03-30T08:39:22Z)

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.