Rate of alignment and communication using quantum systems in the absence of a shared frame of reference
Bibliographic record
Abstract
Quantum information theory is concerned with the storage, transmission, and manipulation of information that is represented in the degrees of freedom of quantum systems. These degrees of freedom are described relative to an external frame of reference. The lack of a requisite frame of reference imposes restrictions on the types of states quantum systems can be prepared in and the type of operations that can be performed on quantum systems. This thesis is concerned with the communication between two parties that lack a shared frame of reference. Specifically, I introduce a protocol whereby the parties can align their respective frames of reference, and a protocol for communicating quantum information in a reference frame independent manner. Using the accessible information to quantify the success of a reference frame alignment protocol I propose a new measure-the alignment rate-for quantifying the ability of a quantum state to stand in place of a classical frame of reference. I show that for the case where Alice and Bob lack a shared frame of reference associated with the groups G=U(1) and G=Z_M (the finite cyclic group of M elements), the alignment rate is equal to the regularized, linearized G-asymmetry. The latter is a unique measure of the frameness of a quantum state and my result provides an operational interpretation of the G-asymmetry that was thus far lacking. In addition, I show that the alignment rate for finite cyclic groups of more than three elements is super-additive under the tensor product of two distinct pure quantum states. The latter is, to my knowledge, the first instance of a regularized quantity that exhibits super-additivity. In addition, I propose a reference-frame-independent protocol for communicating quantum information in the absence of a shared frame of reference associated with a general finite group G. The protocol transmits m logical qudits using r+m physical qudits prepared in a specific state that is reference-frame invariant. Measuring the first r qudits allows one to infer the unitary correction that is required to retrieve the remaining m qudits with perfect fidelity. Moreover, the number of ancillary qudits, r, is finite and depends only the group G associated with the requisite frame of reference. I show that the number of single and two-qubit gates required to encode and decode m logical qudits into m+r physical qudits scales linearly with m and the number of group elements \lvert G\rvert. Furthermore, the number of single and two-qubit gates required per logical qudit m is constant allowing for a more efficient implementation than the best currently known reference frame independent protocols.
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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 | 0.013 | 0.064 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".