SearcharxivSearch

arXiv subjects

Sebastian Zając

Publications and source records attributed to Sebastian Zając.

8 recordsLinked to original sources

The Hermitian inner product selects the time axis, the Born rule measures it

The correspondence between $2\times 2$ Hermitian matrices and Minkowski $4$-vectors recovers Lorentzian symmetries from the internal degrees of freedom of a qubit, with no reference to an external spacetime. Recent work characterises the resulting Lorentz invariants and leaves the \emph{mechanism} of emergence -- what singles out a time direction -- as an explicit open question. We give an elementary answer and, in doing so, correct a natural misattribution. The bare spin space $(\mathbb{C}^2,\varepsilon)$ is $SL(2,\mathbb{C})$-symmetric and singles out no axis; so is the null cone it generates. What selects a future-timelike axis is the choice of a Hermitian inner product, equivalently a positive reference form $σ^0$: this choice -- made in passing from a normed space to a Hilbert space, \emph{before} any probability is assigned -- reduces $SL(2,\mathbb{C})$ to its maximal compact $SU(2)$, the stabiliser of $σ^0$. The Born rule enters one level later: $\langle ξ\vert ξ\rangle = \text{tr}(σ^0 \, ξξ^\dagger)$ is the projection of the state's null vector onto $σ^0$, i.e. its energy in that frame, and under a boost it rescales as a Doppler shift. Thus the Hilbert structure selects the axis; the Born rule is where that axis becomes a measurable energy and where the frame-dependence of $\lvertψ\rvert^2$ becomes empirical. The ingredients are classical; what we add is their identification as the mechanism the recent programme leaves open, with the symmetry-breaking step located precisely. This is a kinematic identification of that step, not a dynamical account of why a particular axis is selected. We close by handing back the many-qubit case, where the datum is a tuple of such choices.

quant-ph

The Inverse Born Rule Equivalence. On the Informational Limits of Real-Valued Amplitude Encodings and the Measurement of Quantum Advantage in Data Embeddings

When does quantum data encoding provide genuine quantum advantage, and when does it merely rephrase a classically solvable problem? We prove an \emph{Equivalence Theorem} demonstrating that any encoding mapping classical data to real-valued amplitudes, $\vertψ_c\rangle = \sum_i c_i \vert i\rangle$ with $c_i \in \mathbb{R}$ and $\sum_i c_i^2 = 1$, composed with a data-independent parameterised unitary and computational-basis measurement, yields exactly the class of classical quadratic forms. We identify the geometric mechanism driving this collapse: the restriction to $\mathbb{R}$ forces a vanishing Berry connection, removing the complex phases required for data-dependent quantum interference. To operationalize this boundary, we introduce encoding diagnostics -- phase complexity $C[Φ]$ and mode-wise von Neumann mutual information $I[Φ]$ -- and link them to the information-geometric excess $Δg$. We show that for all real-valued encodings, $Δg = 0$ identically. We term the misidentification of such models as evidence of quantum computational power the \emph{Inverse Born Rule Fallacy}. Supported by numerical experiments, our results establish that complex-phase structure is a strictly necessary condition for data-driven (Type~B) quantum advantage.

quant-ph

Option Pricing on Noisy Intermediate-Scale Quantum Computers: A Quantum Neural Network Approach

In a global derivatives market with notional values in the hundreds of trillions of dollars, the accuracy and efficiency of pricing models are of fundamental importance, with direct implications for risk management, capital allocation, and regulatory compliance. In this work, we employ the Black-Scholes-Merton (BSM) framework not as an end in itself, but as a controlled benchmark environment in which to rigorously assess the capabilities of quantum machine learning methods. We propose a fully quantum approach to option pricing based on Quantum Neural Networks (QNNs), and, to the best of our knowledge, present one of the first implementations of such a methodology on currently available quantum hardware. Specifically, we investigate whether QNNs, by exploiting the geometric structure of Hilbert space, can effectively approximate option pricing functions. Our implementation utilizes a compact 2-qubit QNN architecture evaluated across multiple state-of-the-art quantum processors, including IBM Fez, IQM Garnet, IonQ Forte, and Rigetti Ankaa-3. This cross-platform study reveals distinct hardware-dependent performance characteristics while demonstrating that accurate pricing approximations can be achieved consistently across different devices despite the constraints of Noisy Intermediate-Scale Quantum (NISQ) hardware. The results provide empirical evidence that QNN-based approaches constitute a viable framework for derivative pricing. While the analysis is conducted within the BSM setting, the broader significance lies in the potential extension of these methods to more realistic and computationally demanding models, including local volatility, stochastic volatility, and interest rate frameworks commonly used in practice.

quant-ph

Predicting Properties of Nodes via Community-Aware Features

This paper shows how information about the network's community structure can be used to define node features with high predictive power for classification tasks. To do so, we define a family of community-aware node features and investigate their properties. Those features are designed to ensure that they can be efficiently computed even for large graphs. We show that community-aware node features contain information that cannot be completely recovered by classical node features or node embeddings (both classical and structural) and bring value in node classification tasks. This is verified for various classification tasks on synthetic and real-life networks.

cs.SI

Lepton masses and mixing in a two-Higgs-doublet model

Within the framework of the two-Higgs Doublet Model (2HDM), we attempt to find some discrete, non-abelian flavour symmetry which could provide an explanation for the masses and mixing matrix elements of leptons. Unlike the Standard Model, currently there is no need for the flavour symmetry to be broken. With the GAP program we investigate all finite subgroups of the U3 group up to the order of 1025. Up to such an order there is no group for which it is possible to select free model parameters in order to match the masses of charged leptons, masses of neutrinos, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix elements in a satisfactory manner.

hep-ph

The flavour problem and family symmetry beyond the Standard Model

In the frame of two Higgs doublet model we try to explain the lepton masses and mixing matrix elements assuming that neutrinos are Dirac particles. Discrete family symmetry groups, which are subgroups of U(3) up to the 1025 order are considered. Like in the one Higgs Standard Model, we found that discrete family symmetries do not give satisfactory answer for this basic questions in the flavour problem.

hep-ph

The discrete family symmetry as a possible solution to the flavour problem

In order to explain the fermions masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-abelian subgroup of $U(3)$ is added to the gauge group $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ . Apart from that, one assumes the existence of one extra Higgs doublet. This article focuses mainly on the mathematical theorems and computational techniques which brought us to the results.

hep-ph

Texture zeros in neutrino mass matrix

The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle θ13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries. Nowadays, assuming one Higgs doublet, it is unlikely that this is still valid. Texture zeroes, that are combined with abelian symmetries, are intensively studied. The neutrino mass matrix is a natural way to study such symmetries.

hep-ph