Quantum

Assignment maps for arbitrary reduced quantum dynamics

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Briefings

A new arXiv preprint establishes a one-to-one correspondence between completely positive trace-preserving (CPTP) maps from an open quantum system to its environment and assignment maps that initialize the composite system in a correlated state. The authors prove that every possible joint state can be realized by these HPTP maps, which sacrifice global positivity. A simple necessary and sufficient condition is derived for local states to belong to the domain of validity, and the geometry of this domain is governed by the joint state assigned to the maximally mixed input, ensuring non-zero volume of admissible local states can coexist with initial entanglement. An operational protocol for witnessing these limits is also provided.

Key points

• The paper establishes a one-to-one correspondence between CPTP maps from an open quantum system to its environment and assignment maps initializing the composite system in a correlated state.
• A simple necessary and sufficient condition is derived for local states to belong to the domain of validity of these assignment maps.

Context

This research provides an operational protocol for witnessing the limits of validity for assignment maps in open quantum systems, addressing a gap in understanding the relationship between local dynamics and global correlations in quantum environments.

Limitations

The evidence is an unverified arXiv preprint (v1) without peer review. The paper does not contain experimental data, specific numerical results, or author names. The findings remain theoretical and do not include any experimental verification or validation.

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