Bounds on probability of transformations between multipartite pure states
Bibliographic record
Abstract
For a tripartite pure state of three qubits, it is well known that there are two inequivalent classes of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) class and the W class. Any two states within the same class can be transformed into each other with stochastic local operations and classical communication with a nonzero probability. The optimal conversion probability, however, is only known for special cases. Here, lower and upper bounds are derived for the optimal probability of transformation from a GHZ state to other states of the GHZ class. A key idea in the derivation of the upper bounds is to consider the action of the local operations and classical communications (LOCC) protocol on a different input state, namely $1/\sqrt{2}[|000\ensuremath{\rangle}\ensuremath{-}|111\ensuremath{\rangle}]$, and to demand that the probability of an outcome remains bounded by 1. We also find an upper bound for more general cases by using the constraints of the so-called interference term and 3-tangle. Moreover, some of the results are generalized to the case in which each party holds a higher dimensional system. In particular, the GHZ state generalized to three qutrits; that is, $|{\mathrm{GHZ}}_{3}\ensuremath{\rangle}=1/\sqrt{3}[|000\ensuremath{\rangle}+|111\ensuremath{\rangle}+|222\ensuremath{\rangle}]$ shared among three parties can be transformed to any tripartite three-qubit pure state with probability 1 via LOCC. Some of our results can also be generalized to the case of a multipartite state shared by more than three parties.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".