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Operations, causality, and memory in continuous time

Fabio Costa

Causalworlds 2026

Grenoble, 21 June 2026

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COST ACTION CA23115

RELATIVISTIC QUANTUM INFORMATION (RQI)

​

20th September 2024- 19th September 2028

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What is COST?

The European Cooperation in Science and Technology (COST) is a funding organisation for the creation of research networks

[…] an open space for collaboration among scientists across Europe (and beyond)

[…] highly interdisciplinary and open.

  • Based in Europe
  • Anyone can participate

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RQI COST action

RQI will apply  quantum information concepts to fundamental problems of relativistic physics

[…] it also aims to incorporate the fundamental principles of relativistic theories into the foundations of QIS […] for theory and technological applications.

 

Join this too!

It’s free.

 

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RQI COST action

  • Chair: C. Anastopoulous
  • Vice-Chair: M. Zych

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Working groups:

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◼ WG1—QFT aspects of Quantum Information�K. Rejzner, V. Vilasini

◼ WG2—Gravitational quantum physics and metrology�D. Rätzel, A. Roura

◼ WG3—Time, causality, and memory in quantum physics�F. Costa, N. Móller

◼ WG4—Dissemination and outreach�M. Christodoulou, D. Terno

◼ WG5—Organization of activities and Implementation of policies�M. Juvilescu, T. R. Perche

​

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What we do

  • (Limited) support for
    • Short-Term Scientific Missions
    • ITC & YRI conference grants
    • Events (workshops/conferences)
  • Online seminars
  • Review articles. WG3:
    • Relational time
    • Event localisation and indefinite causal order
    • Non-Markovianity in quantum metrology
  • Upcoming:
    • Structured debates
    • White papers (idea: key open questions)

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WG3 probable events

Quantum Non-Markovianity II�Stockholm, June 2027

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Observers in Quantum Gravity II

Erlangen, autumn 2027

Check the website:

https://rqi-cost.org/

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Finally out!

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Is causal order an observable?

 

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Continuous operations on non-Markovian processes

FC, Jing Yang, arXiv:2512.05884 [quant-ph]

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Frameworks for quantum causal structures

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Limitation:

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  • Discrete events
  • Instantaneous interventions

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Measurements/causality in QFT?

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Causal structure in GR/QG?

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Finite-time measurements/�continuous monitoring?

This talk

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Repeated measurements?

 

 

*Choi representation

 

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Repeated measurements?

Problem: �system-environment correlations

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Update acts on joint�system-environment state

  • Inaccessible DOFs
  • No independent characterisation operation/process

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Multi-time quantum process

 

 

 

 

Quantum strategy

Process tensor�Superdensity operator

…

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Continuous time

Strategy:

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  • Constructive: system-environment-meter model

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  • Define independent operation/process objects �by tracing out, resp., environment/meter

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  • Derive characterising properties (positivity, causality)

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  • Recover multi-time formalism in discrete-time limit

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WARNING

PATH INTEGRALS ahead

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Coherent-state path integral (unitary)

 

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System-environment-meter model

System

Environment

Meter

 

 

 

 

 

 

 

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Functional Born rule

System

Environment

Meter

 

 

 

 

 

 

 

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Conditional state

System

Environment

Meter

 

 

 

 

 

 

 

 

 

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Process properties �valid for constructive model

 

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Process properties �valid for constructive model

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Process properties �valid for constructive model

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Process properties �valid for constructive model

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Markovianity

 

 

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Recovering multi-time processes

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Recovering multi-time processes

 

 

 

 

 

 

 

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Functional

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Positivity

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Causality

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Markovianity

 

 

 

Multi-time

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Positivity

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Causality

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Markovianity

Recovering multi-time processes

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Alternative approach

  • Finite-dimensional systems
  • Formal limit of Choi operators
  • Continuous matrix product states

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