arXiv subjects

Soumyojyoti Dutta

Publications and source records attributed to Soumyojyoti Dutta.

4 recordsLinked to original sources

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.

quant-ph↗

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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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. We prove that the single-qubit Wigner l_1 metric has a cuboctahedral unit ball, that max_rho C(rho) = (sqrt(3)-1)/2 for a single qubit, attained precisely at the eight face states, and that C(rho_1 x ... x rho_n) <= prod_i (1 + C(rho_i)) - 1 for single-qubit factors. Together these give the exact tensor powers ((1+sqrt(3))/2)^n - 1 and the exact maximum of C over fully separable n-qubit states, leaving only entangled states open. Because no discrete Wigner function for qubits is Clifford covariant, any such measure is frame dependent, and we determine exactly which of its features are not. For a single qubit we show the valid frames are exactly eight, and that C is identical on all of them, so the maxima above are properties of the state rather than of the representation. For two qubits the conclusion reverses: enumerating all 6144 translation-covariant frames, they split into four equal classes on which the ratio C(rho_Rx)/C(rho_Ry) takes the values 1/2, 1 and 2. Within the Wootters frame we compute that structure exactly: a tetrahedral dichotomy governing when the product bound is saturated, and integer values 1, 2, 1 of the tightness ratio kappa := (Gamma-1)/C against the robustness of magic Gamma for three families in the [[2,1,1]] codespace, whose optimal witnesses are logical Pauli operators. We prove the bound Gamma >= 1 + C/M_n, and show C is not a magic monotone, so asymptotic distillation rates require Gamma.

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