Pith Number

pith:XADSYEKL

pith:2026:XADSYEKLZOAHCS454JDUL36XTC

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Purification of a monitored qubit: exact path-integral solution

Henrique Santos Lima, Matheus M. R. Poltronieri Martins

Purification of a monitored qubit reduces to an exactly solvable multiplicative Langevin equation for its purity.

arxiv:2605.12783 v1 · 2026-05-12 · quant-ph · cond-mat.stat-mech

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\pithnumber{XADSYEKLZOAHCS454JDUL36XTC}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

for initial mixed states, the dynamics reduce to a multiplicative Langevin equation for a single scalar parameter representing the state's purity. This stochastic process is solved exactly using the Onsager-Machlup path integral formalism, allowing us to derive the full probability distribution for the qubit's trajectories.

C2weakest assumption

The collisional model of sequential interactions with ancillary qubits faithfully captures continuous-in-time monitoring, and the conditioned evolution of the density matrix can be fully reduced to a single scalar purity parameter without loss of essential information.

C3one line summary

Exact Onsager-Machlup path-integral solution for monitored qubit purification reveals a crossover from diffusion-dominated to measurement-dominated regimes with emergent bimodal purity distributions.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] Y. Li, X. Chen, and M. P. A. Fisher,Quantum Zeno effect and the many-body entanglement transition, Phys. Rev. B98, 205136 (2018) 2018

[2] B. Skinner, J. Ruhman, and A. Nahum,Measurement- Induced Phase Transitions in the Dynamics of Entangle- ment, Phys. Rev. X9, 031009 (2019) 2019

[3] Y. Li, X. Chen, and M. P. A. Fisher,Measurement- driven entanglement transition in hybrid quantum cir- cuits, Phys. Rev. B100, 134306 (2019) 2019

[4] M. J. Gullans and D. A. Huse,Dynamical purifica- tion phase transition induced by quantum measurements, Phys. Rev. X10, 041020 (2020) 2020

[5] C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Lud- wig,Measurement-induced criticality in random quantum circuits, Phys. Rev. B101, 104302 (2020) 2020

Receipt and verification

First computed	2026-05-18T03:09:13.105875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8072c114bcb80714b9de24745efd79881d26fe1fcd056113d9d75c495c9a28b

Aliases

arxiv: 2605.12783 · arxiv_version: 2605.12783v1 · doi: 10.48550/arxiv.2605.12783 · pith_short_12: XADSYEKLZOAH · pith_short_16: XADSYEKLZOAHCS45 · pith_short_8: XADSYEKL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XADSYEKLZOAHCS454JDUL36XTC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b8072c114bcb80714b9de24745efd79881d26fe1fcd056113d9d75c495c9a28b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0be1b1b33ee464d8391b55aa1492043f97159d0aaf663e6069e18c267562304",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-12T21:55:51Z",
    "title_canon_sha256": "8a38f01851dfd4fce251c3f298ddba45f332bb4862895520cb5ed81c506abc66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12783",
    "kind": "arxiv",
    "version": 1
  }
}