Relating non-local quantum computation to information theoretic cryptography
Bibliographic record
Abstract
Non-local quantum computation (NLQC) is a cheating strategy for position-verification schemes, and has appeared in the context of the AdS/CFT correspondence. Here, we connect NLQC to the wider context of information theoretic cryptography by relating it to a number of other cryptographic primitives. We show one special case of NLQC, known as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math>-routing, is equivalent to the quantum analogue of the conditional disclosure of secrets (CDS) primitive, where by equivalent we mean that a protocol for one task gives a protocol for the other with only small overhead in resource costs. We further consider another special case of position-verification, which we call coherent function evaluation (CFE), and show CFE protocols induce similarly efficient protocols for the private simultaneous message passing (PSM) scenario. By relating position-verification to these cryptographic primitives, a number of results in the information theoretic cryptography literature give new implications for NLQC, and vice versa. These include the first sub-exponential upper bounds on the worst case cost of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math>-routing of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>2</mml:mn><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msqrt><mml:mi>n</mml:mi><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mi>n</mml:mi></mml:msqrt><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:math> entanglement, the first example of an efficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math>-routing strategy for a problem believed to be outside <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>y</mml:mi></mml:math>, linear lower bounds on quantum resources for CDS in the quantum setting, linear lower bounds on communication cost of CFE, and efficient protocols for CDS in the quantum setting for functions that can be computed with quantum circuits of low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> depth.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".