Universality of EPR Pairs in Entanglement-Assisted Communication Complexity, and the Communication Cost of State Conversion
Bibliographic record
Abstract
Entanglement assistance is known to reduce the quantum communication complexity of evaluating functions with distributed inputs. But does the type of entanglement matter, or are EPR pairs always sufficient? This is a natural question because in several other settings maximally entangled states are known to be less useful as a resource than some partially entangled state. These include non-local games, tasks with quantum communication between players and referee, and simulating bipartite unitaries or communication channels. By contrast, we prove that the bounded-error entanglement-assisted quantum communication complexity of a function cannot be improved by more than a constant factor by replacing maximally entangled states with arbitrary entangled states. In particular, we show that every quantum communication protocol using $Q$ qubits of communication and arbitrary shared entanglement can be $ε$-approximated by a protocol using $O(Q/ε+\log(1/ε)/ε)$ qubits of communication and only EPR pairs as shared entanglement. Our second result concerns an old question in quantum information theory: How much quantum communication is required to approximately convert one pure bipartite entangled state into another? We show that the communication cost of converting between two bipartite quantum states is upper bounded, up to a constant multiplicative factor, by a natural and efficiently computable quantity which we call the $\ell_{\infty}$-Earth Mover's Distance (EMD) between those two states. Furthermore, we prove a complementary lower bound on the cost of state conversion by the $ε$-smoothed $\ell_{\infty}$-EMD, which is a natural smoothing of the $\ell_{\infty}$-EMD that we will define via a connection with optimal transport theory.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.040 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.004 | 0.017 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".