Does multiplicity-space coherence improve STP protocols?
Within one total-spin sector, compare a state with its dephased version in a fixed coupling basis. Seek a separation in task success probability or measurement cost.
Discuss this questionFix a total-spin sector and a stated nested-subsystem coupling basis. Compare coherent multiplicity states with states dephased in that basis for a defined computational task under STP. Seek an operational separation and determine how it depends on the choice of coupling basis.
Why this is interesting
Low total spin is only a label. Coherence among compatible coupling paths can be relevant even when that label never changes; coherence between distinct global-spin sectors is a different issue for invariant operations.
Explicit variants
A precise first comparison
Choose real density matrices in one total-spin sector and a fixed nested coupling basis. Compare with its dephased state using the same STP decision or discrimination task, ancilla budget, and measurement count. Establish a quantitative success gap or cost separation. This is a within-sector coherence question; it does not assume that STP can prepare every candidate state.
Delocalization across incompatible subsystems
At a fixed global spin, define a restriction on the distribution of spin information across overlapping subsystems, such as a bounded-size cluster preparation ansatz. Does that restriction imply efficient simulation or prevent a specified STP task? Conversely, identify states and protocols for which correlations across incompatible subsystem decompositions are necessary for an advantage.
A place to start
Use the two-dimensional four-spin singlet multiplicity space to find an overlapping-pair measurement that distinguishes a coherent state from its dephased counterpart.
Related work
These works provide context and established results. They need not be the origin of this exact formulation.
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