arXiv subjects

Tony Newton

Publications and source records attributed to Tony Newton.

5 recordsLinked to original sources

arXiv2026

Stochastic Orders of the Exit Pair and the Monotone Response to Resetting

Resetting a process, that is, restarting it from its initial position at random times, changes the probability that it leaves an interval through one end rather than the other. We show that the direction of this change is governed by how the exit time depends on the exit side, and we express this through classical stochastic orders. For random walks and birth-death chains we determine when resetting more intensively always moves the exit probability in the same direction, and we show that this can fail: we give an explicit chain in which the direction reverses twice over time, and bound the number of such reversals spectrally. We also show how the direction depends on the starting point. In the continuum limit we obtain the corresponding results for diffusions with drift.

math.PR↗

arXiv2026

Distributed Phase Tags: A Locality-Preserving Realification Compiler for Misty-State Quantum Programs

Complex amplitudes can be simulated over real Hilbert spaces by adjoining a two-dimensional real/imaginary degree of freedom. In a multipartite program, however, one globally shared phase tag is not a locality-preserving program transformation: every party would have to act on the same auxiliary system. We recast the distributed real simulation of multipartite quantum mechanics as a syntax-directed compiler into a real misty-state intermediate language. For $n$ parties we give explicit phase-reference codewords $|0\rangle_{P_n}$ and $|1\rangle_{P_n}$ on $n$ local tags and prove that the same real operator $J=XZ$ on any single tag realizes the logical action of multiplication by $i$. If a complex party-local gate is $A=A_R+iA_I$, its real translation is \[ \widehat A_j=A_R\otimes I+A_I\otimes J_j, \] which acts only on party $j$'s data and local phase tag. We prove an intertwining theorem for arbitrary finite party-local pure-state circuits, exact preservation of computational-basis measurement probabilities, preservation of the run-time interaction graph, and one-rebit-per-party overhead. For the canonical three-party GHZ program, the translation lies entirely inside the ordinary black-and-white misty gate fragment: controlled-$J$ replaces the complex phase operation, while the invariant $J_jJ_k|0\rangle_P=-|0\rangle_P$ transfers the required branch sign. This yields a short correctness proof for all four promised GHZ inputs and explains the earlier 64-path cancellation calculation at a single logical phase-code boundary. We distinguish this program realification problem from the weaker task of finding any real strategy with the same correlations, and state precisely which parts are known real-Hilbert-space simulation and which parts belong to the misty-language compilation layer developed here.

quant-ph↗

arXiv2026

The GHZ Game in Black and White

We show that it is possible for three people to win the GHZ game with just the standard real valued misty state formalism, but each party will need to have two balls instead of one. That is, there will be six balls involved, rather than three. In fact, as a general rule, instead of using complex numbers in a quantum computer you can always add a qubit to "tag" complex numbers. But for proofs of non-locality, like the GHZ game, we cannot have a single universal tagging qubit, because all three parties would need access to it and therefore they could potentially transfer information via it. That's where we need to replace the one ball with three that each only need to be accessed locally.

quant-ph↗

arXiv2026

All-Minors Matrix-Tree Theory for Superport Networks: Completed Quotient-Incidence Determinants and Conductance-Weighted Subdivision Extensions

An electrical network can be summarized at its boundary by a response matrix: prescribed boundary voltages determine boundary currents. A superport network adds a constraint by grouping boundary terminals into superports, requiring the total current in each group to be zero and making voltage differences inside the groups the natural coordinates. Earlier work determined forest formulas for a single response entry and for the determinant of the whole response matrix. The missing case was an arbitrary subdeterminant, or minor: one needs to know not only which spanning forests contribute, but also the sign carried by each forest. This paper supplies that sign rule. After choosing one reference vertex in each superport, the response is \[ L=\left(D^{T}K^{-1}D\right)^{-1}, \] with $K$ the grounded weighted Laplacian and $D$ recording the selected voltage differences. Contracting the components of a physical spanning forest $F$ produces a much smaller quotient port graph $H_F$. Its reduced incidence matrix \[ B_F=Q_FD \] has columns only of the forms \[ 0,\qquad \pm e_a,\qquad e_a-e_b. \] Hence every square incidence minor is exactly $0$ or $\pm1$. For a $k$-set of response coordinates $I$, append to $B_F$ the selector rows $E_I^{T}$ and define the completed quotient-incidence determinant \[ \widehatχ_F(I) = \det \begin{pmatrix} B_F\\ E_I^{T} \end{pmatrix}. \] For coordinate sets $I,J$ of the same size, the arbitrary response minor is a weighted spanning-forest sum whose coefficient is simply \[ \widehatχ_F(I)\widehatχ_F(J). \] Thus the Jacobi complementary-minor factors used in the derivation disappear from the final theorem. Direct block-triangular reduction gives \[ \widehatχ_F(I)\in\{0,\pm1\}, \] with nonvanishing occurring exactly when the complementary quotient edges $N\setminus I$ form a spanning tree of $H_F$.

math.CO↗

arXiv2026

Certified Misty-State Rewriting (A Question-and-Answer Guide)

Quantum mechanics is difficult to teach because its conceptual content and mathematical notation usually arrive together. Rudolph's misty-state language was designed to decouple those burdens; basis states are visual objects, clouds represent superposition, gates act by elementary replacement rules, and destructive interference appears as cancellation rather than as matrix calculation. An elementary ``misty-state'' language can make quantum circuits accessible to students before they master complex linear algebra. Development presented here was initiated/led by the first author. The contribution is not a replacement for complete graphical calculi such as ZX or sum-over-paths. It is a source-specific bridge from an intuitive educational notation to a mathematically explicit, executable, and falsifiable semantics.

physics.pop-ph↗