arXiv subjects

Soumyojyoti Dutta

Publications and source records attributed to Soumyojyoti Dutta.

4 recordsLinked to original sources

arXiv2026

A Phase-Space Geometric Measure of Magic in Qubit Systems

Magic -- the resource enabling quantum computational advantage beyond stabilizer circuits -- has a clean phase-space characterization in odd prime dimensions that qubits notoriously lack. We study C(rho), the l_1 distance from a state's discrete Wigner function to the stabilizer polytope, and determine its exact geometry. For a single qubit with Bloch vector r we prove the closed form C = max(0, ||r||_1 - 1)/2, so the maximum is (sqrt(3)-1)/2, attained at the eight face states. For products of single-qubit states, C(rho_1 x ... x rho_n) <= prod_i (1 + C(rho_i)) - 1, with equality whenever every factor has Bloch sign product r_x r_y r_z <= 0; this includes the exact tensor powers ((1+sqrt(3))/2)^n - 1 and the exact maximum of C over fully separable n-qubit states. Because no discrete Wigner function for qubits is Clifford covariant, any such measure is frame dependent, and we identify which of its features are not. For a single qubit there are exactly two valid frames up to phase-space translation and C is identical on both. Pauli-covariant two-qubit frames number 2048 up to translation, and across them the ratio C(rho_Rx)/C(rho_Ry) takes the values 1/2, 1 and 2. In every one of these frames some stabilizer state has negative Wigner entries, a consequence of the Mermin-Peres square, so the two-qubit bound Gamma >= 1 + C/2 against the robustness of magic Gamma is frame independent. Within the Wootters frame we prove integer values 1, 2, 1 of the tightness ratio kappa := (Gamma-1)/C for three families in the two-qubit repetition codespace, with explicit certificates. For n-qubit GHZ phase states we prove Gamma = |sin phi| + |cos phi| for all n and C >= 2^(floor(n/2)-1) (|sin phi| + |cos phi| - 1), tight for n = 2 and, by exact linear programming, for n = 3, 4, so kappa decays exponentially. Finally, C is not a magic monotone, so it cannot replace Gamma in distillation bounds.

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arXiv2026

Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement

We introduce Magic Secret Sharing (MSS), a quantum cryptographic primitive in which the secret is the computational capability of a quantum state rather than its classical description. In the resource theory of magic, non-stabilizer states fuel universal quantum computation via non-Clifford gates; MSS distributes this resource with an (n-1,n) threshold structure using a pre-shared GHZ state and a single local phase gate P(phi) = diag(1, exp(i*phi)). Any individual party holds the maximally mixed state I/2, with Wigner distance C(I/2) = 0, so no local operation can yield non-Clifford computational advantage regardless of what operations are applied or what noise acts on the device. The authorised coalition reconstructs magic content C(phi) = (|sin(phi)| + |cos(phi)| - 1)/2 exactly, enabling a logical T gate via gate teleportation in multi-server blind quantum computation (BQC). Among diagonal parametric gates, phase gates are the unique class satisfying the security condition, characterised via an exact column-sum condition. The protocol is elevated to a one-sided device-independent (1SDI) setting via a steering inequality: the assemblage produced on the recipient's side certifies magic delivery without trusting the coalition's devices. We demonstrate the (2,3) instance on ibm_marrakesh (156-qubit IBM Heron): security (C(rho_Bob) < 10^-6, the linear-programming solver tolerance) holds in every run and is independently reproduced on a second qubit assignment, and state fidelity reaches 0.959-0.973 for the authorised party, with faithfulness confirmed for all four test values of phi to within 0.025 in magic content, a residual that depolarising noise alone accounts for.

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arXiv2026

Perfect State Transfer from a Localised Two-Excitation State to a Dicke State via Static Spin-Network Hamiltonians

I construct a family of time-independent, excitation-preserving spin Hamiltonians realising perfect state transfer from a localised two-excitation state to the symmetric two-excitation Dicke state, for every $N\ge4$. The Hamiltonian has the physical form $H=\sum_{i<j}J_{ij}(σ_i^+σ_j^-+σ_j^+σ_i^-)+\sum_iε_i n_i$ with real couplings, and satisfies $e^{-iHt}|110\cdots0\rangle=e^{iϕ}|D_N^{(2)}\rangle$ at a finite time. An $S_{N-2}$ permutation symmetry on the unoccupied spins reduces the dynamics to a four-dimensional invariant subspace. Requiring $(|ψ_0\rangle+|D_N^{(2)}\rangle)/2$ to be a zero eigenvector fixes the on-site energies in closed form and leaves three coupling parameters free. The inverse spectral problem then becomes two polynomial equations in two coupling ratios; eliminating one gives a degree-six reciprocal polynomial, which $z=x+x^{-1}$ converts to a cubic. For the spectral family $(-n,-1,1)$ with odd $n$, factorising the cubic's leading coefficient and evaluating it at $z=-2$ shows that some odd $n$ always produces a real root below $-2$, which a subresultant lifts back to the original system. The existence argument is symbolic and uses no numerical optimisation. Since that coefficient contains no odd powers of $n$, the required $n$ comes with an explicit threshold, not an asymptotic guarantee. I also cost the construction: couplings grow as $N^{1/2}$ and the on-site range as $N^{3/2}$, the transfer time stays within a factor 2.3-3.0 of the Mandelstam-Tamm limit at every size, and the fidelity is sensitive to systematic drift of the spectator-spectator coupling class but tolerant of independent bond disorder, which self-averages. This is a constrained analogue of perfect state transfer: for general real states an unconstrained real symmetric matrix suffices, whereas here the Hamiltonian must have excitation-preserving spin-network form.

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arXiv2026

Universal Z-only Correction for Distributing Arbitrary Graph States in Quantum Networks

Distributing arbitrary graph states across quantum networks is a central challenge for modular quantum computing and measurement-based quantum communication. I present a protocol converting |E| elementary two-qubit resource states -- one per edge of the target graph G = (V,E) -- into the distributed graph state |G>, using only operations local to each party (single-qubit gates, CZ gates between a party's own data and resource qubits, single-qubit measurements) and classical communication, and reaching arbitrary topologies, not just the GHZ class of prior walk-based schemes. The central result is a universal correction theorem: for any graph and any measurement outcome, the local correction C_v = Z_v^{g_v}, with g_v the XOR of the far-side outcomes on edges at v, restores the state to |G>. The elementary step is the coined discrete-time quantum walk with the position-permuting shift replaced by a diagonal CZ gate: the phase quantum walk (PQW). The correction is verified exhaustively on 22 connected graphs (32,212 outcomes) at F = 1.0. Exact closed-form fidelities under independent depolarising and phase damping noise on the resource qubits follow, F*_dep = prod_v [1 + (1 - 4p/3)^{deg v}]/2 and F*_pd = prod_v [1 + (1 - p)^{(deg v)/2}]/2: the noise budget is set by the degree sequence, not by edge count alone. On ibm_kingston direct fidelity estimation certifies F = 0.815(3) for |L_4>, 0.776(3) for |GHZ_4>, and 0.733(3) for |C_4>. A necessary condition for SWAP-free execution at coupling girth gamma follows: target girth at least gamma/3 and maximum degree at most 3. On heavy-hex this forbids triangles and places the canonical circuits for P_4, C_4 and K_4 in a strict embeddability hierarchy -- flexible, rigid, non-embeddable. The obstruction constrains the circuit, not the state: |K_4> is LC-equivalent to the star and remains reachable on the native star layout.

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