Witnessing environment dimension through temporal correlations
arXiv:2305.19175 · doi:10.22331/q-2024-01-10-1224
Abstract
We introduce a framework to compute upper bounds for temporal correlations achievable in open quantum system dynamics, obtained by repeated measurements on the system. As these correlations arise by virtue of the environment acting as a memory resource, such bounds are witnesses for the minimal dimension of an effective environment compatible with the observed statistics. These witnesses are derived from a hierarchy of semidefinite programs with guaranteed asymptotic convergence. We compute non-trivial bounds for various sequences involving a qubit system and a qubit environment, and compare the results to the best known quantum strategies producing the same outcome sequences. Our results provide a numerically tractable method to determine bounds on multi-time probability distributions in open quantum system dynamics and allow for the witnessing of effective environment dimensions through probing of the system alone.
arXiv comment24 pages, 7 figures
References in corpus (51)
- Separability Criterion for Density Matrices
- Quantum sensing
- Entanglement detection
- Non-Markovian dynamics in open quantum systems
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Open Quantum Systems. An Introduction
- Bell Inequalities and the Separability Criterion
- Quantum correlations with no causal order
- Quantum computations without definite causal structure
- Theoretical framework for quantum networks
- Unknown Quantum States: The Quantum de Finetti Representation
- A complete family of separability criteria
- Leggett-Garg Inequalities
- Distinguishing separable and entangled states
- Non-Markovian quantum processes: complete framework and efficient characterisation
- Individual quantum probes for optimal thermometry
- Device-independent tests of classical and quantum dimensions
- Non-perturbative treatment of non-Markovian dynamics of open quantum systems
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound
- One-and-a-half quantum de Finetti theorems
- Spin squeezing inequalities and entanglement of qubit states
- Thermometry in the quantum regime: Recent theoretical progress
- Quantum stochastic processes and quantum non-Markovian phenomena
- Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems
- Dimension witnesses and quantum state discrimination
- Quantum correlations in the temporal CHSH scenario
- Evaluation of convex roof entanglement measures
- Bounding the quantum dimension with contextuality
- Impurities as a quantum thermometer for a Bose-Einstein condensate
- Simulation complexity of open quantum dynamics: Connection with tensor networks
- The power of symmetric extensions for entanglement detection
- Semidefinite Programming in Quantum Information Science
- Maximum violations of the quantum-witness equality
- Witnessing quantum memory in non-Markovian processes
- Markovian embedding of non-Markovian quantum collisional models
- Structure of temporal correlations of a qubit
- On quantum estimation, quantum cloning and finite quantum de Finetti theorems
- Leggett-Garg Macrorealism and temporal correlations
- Semidefinite programming hierarchies for constrained bilinear optimization
- Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
- Memory cost of temporal correlations
- Modelling and Filtering for Non-Markovian Quantum Systems
- Quantum-Inspired Hierarchy for Rank-Constrained Optimization
- Temporal correlations in the simplest measurement sequences
- Simulating extremal temporal correlations
- Ticking-clock performance enhanced by nonclassical temporal correlations
- Quantum filter for a class of non-Markovian quantum systems
- Certifying dimension of quantum systems by sequential projective measurements
- Quasi-polynomial time algorithms for free quantum games in bounded dimension