**A. Quantum Secret Sharing**

Quantum Secret Sharing (QSS) is a procedure for splitting a message into several parts so that no single subset of parts is sufficient to read the message, but the entire set is. This can also naturally be extended to Quantum Operation Sharing (QOS). In this section, quantum secret sharing using the 7 qubit XZW resource-state is proposed, with three proposals for the same.

#### **A.1 Proposal 1**

Let us consider the situation in which Alice possesses the 1st qubit, Bob possesses qubits 2, 3, 4, 5, 6 and Charlie possesses the 7th qubit. Alice has an unknown qubit *α*∣0i þ *β*∣1i which she wants to share with Bob and Charlie.

Now, Alice combines the unknown qubit with ∣Ψ7i and performs a Bell measurement, and conveys her outcome to Charlie by two classical bits. For instance if Alice measures in the ∣Φþi basis, then the Bob-Charlie system evolves into the entangled state.

$$\begin{aligned} a|100001\rangle - a|000100\rangle - a|000011\rangle - a|001001\rangle \\ + a|001010\rangle + a|010101\rangle - a|010110\rangle - a|011000\rangle \\ + a|011011\rangle + a|100010\rangle + a|101100\rangle + a|101111\rangle - \\ a|110011\rangle + a|11101\rangle - a|111110\rangle + \beta|000000\rangle \\ + \beta|0000011\rangle + \beta|001101\rangle + \beta|010001\rangle \\ - \beta|010100\rangle + \beta|011100\rangle - \beta|01111\rangle - \beta|100101\rangle - \\ \beta|0000000\rangle - \beta|100110\rangle + \beta|101000\rangle + \beta|101011\rangle \\ + \beta|110100\rangle - \beta|110111\rangle - \beta|111001\rangle + \beta|111010\rangle \\ \end{aligned} \tag{A1}$$

Now, Bob can perform a five-qubit measurement and convey his outcome to Charlie through a classical channel. Having known the outcome of both their measurement, Charlie will obtain a certain single qubit quantum state. The outcome of the measurement performed by Bob is correlated with the state obtained by Charlie. If Bob measures ∣*A*�i then Charlie obtains the state *α*∣0i � *β*∣1i, while if Bob measures the state ∣*B*�i then Charlie obtains the state *β*∣0i � *α*∣1i, where

∣*A*�i

$$\begin{aligned} &= -|00010\rangle + |00101\rangle - |01011\rangle - |01100\rangle \\ &+ |10001\rangle + |10110\rangle - |11111\rangle \pm (|000001\rangle \\ &+ |00110\rangle + |01000\rangle - |01111\rangle - |10010\rangle \\ &+ |10101\rangle - |11011\rangle - |11100\rangle) \end{aligned} \tag{A2}$$

$$\begin{aligned} \vert B \pm \rangle \\ &= \pm (\vert 10000 \rangle - \vert 00011 \rangle - \vert 00100 \rangle + \vert 01010 \rangle \\ &+ \vert 01101 \rangle + \vert 10111 \rangle - \vert 11001 \rangle + \vert 11110 \rangle) \\ &+ \vert 000000 \rangle + \vert 00111 \rangle - \vert 01001 \rangle + \vert 01110 \rangle \\ &- \vert 000000 \rangle - \vert 10011 \rangle + \vert 10100 \rangle + \vert 11010 \rangle \\ &+ \vert 11101 \rangle \end{aligned} \tag{A3}$$
