Q31: How can a symmetric block acquire lower subsystem spin?

Working mathematical formulation

Start a $k$ -qubit block in $P_{\mathrm{sym},k}/(k+1)$ . Supply $m$ fresh maximally mixed qubits or specified independently prepared invariant blocks, and allow adaptive STP on a stated interaction graph. For a designated retained subsystem $S$ , bound the measurements, supplied qubits, discarded qubits, and success probability needed to obtain $\Pr(J_S\le j^*)\ge 1-\varepsilon.$ Compare these achievable tradeoffs as a function of $k,m,j^*,\varepsilon$ .

Scope & assumptions

With $m=0$ and only internal STP, the state is unchanged and no lower-spin outcome occurs. A Markov description of selected spin labels needs a justified closure property; the omitted multiplicity state can retain memory. Discarding alone from a fully symmetric register also leaves a fully symmetric retained subsystem.

Why this is interesting

This preserves the proposed picture of a process starting from symmetry while identifying the operations that can actually change it. Relative structure between independently prepared blocks can become useful even when each block is internally symmetric.

A place to start

Study $\frac{P_{\mathrm{sym},3}}4\otimes\frac I2$ and measure across the block boundary. Compare its branches with the four-qubit mixed-input figure; distinguish changing subsystem spin from changing the total spin of a closed register.

Related work

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

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Why this is interesting

A place to start

Related work

Related questions

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