Simple and maximally robust processes with no classical common-cause or direct-cause explanation

Abstract

Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause process is not equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

arXiv comment24+8 pages, 11 figures. Code available at https://github.com/marcellongvb/non_ccdc_processes

References in corpus (48)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement detection
• Separability criterion and inseparable mixed states with positive partial transposition
• Quantum correlations with no causal order
• General Entanglement Breaking Channels
• Robustness of entanglement
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Quantum steering: a review with focus on semidefinite programming
• A complete family of separability criteria
• Quantum Circuits Architecture
• Distinguishing separable and entangled states
• Concepts of quantum non-Markovianity: a hierarchy
• Transforming quantum operations: quantum supermaps
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Experimental Superposition of Orders of Quantum Gates
• Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
• Operational Markov condition for quantum processes
• Experimental Verification of an Indefinite Causal Order
• Quantum causal modelling
• Quantum Channels with Memory
• Witnessing causal nonseparability
• Simulating positive-operator-valued measures with projective measurements
• Quantum stochastic processes and quantum non-Markovian phenomena
• Genralized Robustness of Entanglement
• Inferring causal structure: a quantum advantage
• Toward a general theory of quantum games
• Operational approach to open dynamics and quantifying initial correlations
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• General method for constructing local-hidden-variable models for entangled quantum states
• The power of symmetric extensions for entanglement detection
• Quantum measurement incompatibility does not imply Bell nonlocality
• Algorithmic construction of local hidden variable models for entangled quantum states
• An introduction to operational quantum dynamics
• Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• Measurement incompatibility does not give rise to Bell violation in general
• Quantum-coherent mixtures of causal relations
• Most incompatible measurements for robust steering tests
• Witnessing quantum memory in non-Markovian processes
• Entanglement, non-Markovianity, and causal non-separability
• Incompatible quantum measurements admitting a local hidden variable model
• Genuine Multipartite Entanglement in Time
• Causally nonseparable processes admitting a causal model
• Experimental Demonstration of Instrument-specific Quantum Memory Effects and Non-Markovian Process Recovery for Common-Cause Processes
• Quantum superpositions of "common-cause" and "direct-cause" causal structures
• Memory Effects in Quantum Processes

Cited by in corpus (12)

• Genuine Multipartite Entanglement in Time
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Resource theory of causal connection
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Local disclosure of quantum memory in non-Markovian dynamics
• Certifying Quantum Separability with Adaptive Polytopes
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Semi-device-independent certification of quantum non-Markovianity using sequential Random Access Codes
• Hamiltonian characterisation of multi-time processes with classical memory
• Entanglement-breaking channels are a quantum memory resource
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states