Q27: How accurately can physical devices implement singlet–triplet projection?

Working mathematical formulation

For a proposed physical singlet/triplet readout, characterize the full quantum instrument and its distance from the ideal singlet/triplet projections $\rho\mapsto P_s\rho P_s$ and $\rho\mapsto P_t\rho P_t$ . Quantify destructive loss, leakage, unwanted resolution within the triplet sector, and repeatability.

Scope & assumptions

Testing two independent coherences is an illustrative diagnostic; it does not certify a general channel on the three-dimensional triplet space.

Why this is interesting

Matching singlet/triplet outcome probabilities does not guarantee the coherence needed for repeated adaptive computation.

Explicit variants

Direct readout versus gate-mediated implementation
For a named platform, compare a direct singlet/triplet measurement that keeps the measured qubits with an ancilla-controlled-SWAP construction at the same instrument error. Include loss, latency, connectivity, repeated-measurement cost, and the overhead of a complete encoded task. Favorable outcome fidelity alone is insufficient.

A place to start

Use a tomographically complete family of inputs, including triplet superpositions, to reconstruct the outcome probabilities and conditional state changes. Compare the full measurement with ideal STP, alongside its outcome fidelity.

Related work

These works provide context and established results. They need not be the origin of this exact formulation.

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