Pith Number

pith:I4UX2DYH

pith:2026:I4UX2DYHXAQOVSLYIUIFJH6BFG

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Resource theory of coherence in continuous position basis from measurement-induced dephasing

Fabio Costa, Karol Sajnok

Quantum coherence in the continuous position basis is disturbance under a momentum-kick dephasing channel rather than distance from diagonal states.

arxiv:2605.09014 v2 · 2026-05-09 · quant-ph · math-ph · math.MP

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Claims

C1strongest claim

We develop a resource-theoretic framework for quantum coherence directly in continuous basis, with emphasis on the position representation... This yields a fixed-point notion of incoherence and a natural class of dephasing-covariant free operations. For physically relevant kernels, however, the fixed-point set contains no normal states, showing that continuous-basis coherence is tied to dephasing disturbance rather than to distance from a nonempty set of diagonal states.

C2weakest assumption

The assumption that a dephasing channel based on random momentum kicks (equivalently, unconditional back-action of a finite-resolution position measurement) provides a suitable and physically motivated definition of incoherence for normal states in the continuous position basis, since standard finite-dimensional dephasing maps cannot be transferred directly due to non-normalizable position eigenstates. This premise is introduced in the abstract as the foundation for the entire framework.

C3one line summary

Develops a resource-theoretic framework for coherence in continuous position basis using a measurement-induced dephasing channel, defining quantifiers, witnesses, and an application to Gaussian wavepackets in gravitational potentials.

References

50 extracted · 50 resolved · 4 Pith anchors

[1] bound coherence

[2] However, it fails (v), givingC l1(|Ψd⟩) =d−1for maximally coher- ent states instead oflogd

[3] The trace-norm case (p= 1) is contractive and thus satisfies (i), (ii), and (iv), but it fails strong monotonicity (iii) under IO[19]

[4] Comparison of Properties The main properties of the measures discussed above are summarized in Table I. It is evident that the relative entropy of coherence stands out as the only quantifier satisfyin

[5] The squared norm of a linear map is convex, henceC g 2 is convex. E. Uniqueness on pure states In discrete systems with idempotent dephasing∆, S(ρ∥∆(ρ)) =S(∆(ρ))for pure states. In the continuous case

Formal links

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Receipt and verification

First computed	2026-05-20T00:00:41.804063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47297d0f07b820eac9784510549fc129a0c26898791a3fc70405cc193a7ae671

Aliases

arxiv: 2605.09014 · arxiv_version: 2605.09014v2 · doi: 10.48550/arxiv.2605.09014 · pith_short_12: I4UX2DYHXAQO · pith_short_16: I4UX2DYHXAQOVSLY · pith_short_8: I4UX2DYH

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/I4UX2DYHXAQOVSLYIUIFJH6BFG \
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# expect: 47297d0f07b820eac9784510549fc129a0c26898791a3fc70405cc193a7ae671

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "1790231aa92d73f8dd8795e6dd409a53a0f393122571b7c787a3216ebe09e257",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-09T15:53:59Z",
    "title_canon_sha256": "ad58b69e198cec39b2dc2ba1be512879d0b86ad487fd2e4a81953c313cb37d01"
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  "source": {
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    "kind": "arxiv",
    "version": 2
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