arXiv subjects

Zafer Gedik

Publications and source records attributed to Zafer Gedik.

15 recordsLinked to original sources

arXiv2026

The Quad-$C_5$ Graph: Maximum Contextuality Gap on Eight Vertices

Quantum contextuality rules out classical descriptions in which measurement outcomes are independent of the compatible measurements performed alongside them. While the KCBS pentagon provides the minimal qutrit test, identifying larger but still compact contextuality witnesses remains important for understanding how contextuality can be organized, amplified, and benchmarked. We solve the eight-event version of this problem within the graph-theoretic framework for contextuality. An exhaustive search over all 11,117 connected non-isomorphic graphs with eight vertices identifies a sparse ten-edge graph, which we call Quad-$C_5$, as the maximum-gap witness. The graph has a larger absolute contextuality gap than the Wagner graph, a standard eight-vertex benchmark, despite having fewer exclusivity relations. Its structure is transparent: it is formed from four overlapping KCBS pentagons, with each edge shared by two pentagons. We prove that Quad-$C_5$ is already contextual for a single qutrit by giving an explicit three-dimensional construction. In this qutrit realization its contextuality margin equals that of KCBS, whereas its full quantum advantage is reached numerically in four dimensions and exceeds that of the Wagner graph. Quad-$C_5$ therefore provides a compact bridge between minimal qutrit contextuality and stronger four-dimensional contextuality witnesses.

quant-ph↗

arXiv2026

Contextuality from the Projector Overlap Matrix

We place several known indicators of Kochen--Specker contextuality -- the KCBS correlator $\chi$, the contextual fraction $\CF$, the Shannon-entropic $n$-cycle inequality of Chaves and Fritz, and the operational commutator witness $D$ of Paper~I -- into a single projector-geometric framework organized around the overlap matrix $\Tcal_{ij} = d^{-1}\tr[(\hat P_i \hat Q_j)^2]$, where $\hat P_i$ and $\hat Q_j$ are the joint-eigenspace projectors of the two compatible observable pairs within a measurement context. The state-independent scalar content of $\Tcal$ is carried by two independent contractions: the mutual information energy $E = \sum_{ij}\Tcal_{ij}$ of Paper~I (equivalently, its logarithmic form $S_2 = -\log_2 E$), and the Maassen--Uffink extremal overlap $c_\MU = \max_{i,j}|\langle a_i,b_i | c_j,b_j\rangle|$. We prove that $S_2$ is non-increasing under coarse-graining, that $S_2(\Gcal) > 0$ is a necessary configuration-level condition for observable contextuality, and that the additive composition $S_2(\Gcal) = \sum_\alpha S_2(\Gcal_\alpha)$ is exact for the KCBS pentagon. We further show that in the spin-$1$ realization of the KCBS pentagon, a shared $m_s=0$ eigenstate in each context forces $c_\MU = 1$, rendering every Maassen--Uffink-type bound trivial -- a structural mechanism that makes explicit why outcome-entropic uncertainty relations based on $c_\MU$ are silent on KCBS contextuality, while $S_2 \approx 2.7266$~bits throughout. Applied to KCBS and CHSH, the framework identifies regimes in which every state-dependent witness considered here is silent yet $S_2(\Gcal) > 0$ by an amount set by the projector geometry alone.

quant-ph↗

arXiv2026

Non-Associativity Induced Modifications of Open-System Quantum Dynamics: General Master Equation and a Two-Qubit Ising Case Study

Nonassociative deformations of phase-space structures arise naturally in the presence of magnetic charge, where the Jacobi identity for momentum components fails and the corresponding Moyal product becomes nonassociative. While such structures are well understood at the level of single-particle kinematics, their implications for open-system quantum dynamics remain largely unexplored. Here we derive a Born-Markov master equation for a system coupled to a bath when the underlying operator product is weakly nonassociative. The deformation enters through associators appearing in the second-order kernel, while pairwise operator products and dissipators retain their standard form. The resulting correction is dispersive and modifies the Liouville-von Neumann part of the generator without introducing additional dissipative channels. We then embed this structure into a two-qubit transverse-field Ising model using a Stratonovich-Weyl representation and an Ising-aligned twisted Poisson structure. In the zero-temperature limit, the nonassociative terms produce a nonlinear correction in which the instantaneous population imbalance of each qubit feeds back into the dynamics as a state-dependent longitudinal field. Numerical simulations in the weak-coupling regime, where the Born-Markov derivation is quantitatively controlled, show that increasing the nonassociativity parameter suppresses steady-state entanglement by up to 59%, reduces purity, and increases entropy, while leaving the relaxation timescale set by the dissipative rates unchanged. These results demonstrate that weak nonassociativity manifests as a coherent, population-dependent deformation of open-system dynamics rather than an additional dissipative mechanism.

quant-ph↗

arXiv2026

Fidelity-Age-Aware Scheduling in Quantum Repeater Networks

Quantum repeater networks distribute entanglement over long distances but must balance fidelity, delay, and resource contention. Prior work optimized throughput and end-to-end fidelity, yet little attention has been paid to the freshness of entanglement-the time since a usable Bell pair was last delivered. We introduce the Fidelity-Age (FA) metric, which measures this interval for states whose fidelity exceeds a threshold Fmin. A renewal formulation links slot-level success probability to long-run average FA, enabling a stochastic control problem that minimizes FA under budget and memory limits. Two lightweight schedulers, FA-THR and FA-INDEX, approximate Lyapunov-drift-optimal control. Simulations on slotted repeater grids show that FA-aware scheduling preserves throughput while reducing extreme-age events by up to two orders of magnitude. Fidelity-Age thus provides a tractable, physically grounded metric for reliable and timely entanglement delivery in quantum networks.

quant-ph↗

arXiv2025

Information-Theoretic and Operational Measures of Quantum Contextuality

We propose an information -- theoretic framework for quantifying Kochen-Specker contextuality. Two complementary measures are introduced: the mutual information energy, a state-independent quantity inspired by Onicescu's information energy that captures the geometric overlap between joint eigenspaces within a context; and an operational measure based on commutator expectation values that reflects contextual behavior at the level of measurement outcomes. We establish a hierarchy of bounds connecting these measures to the Robertson uncertainty relation, including spectral, purity-corrected, and operator norm estimates. The framework is applied to the Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) scenario for spin-1 systems, where all quantities admit closed-form expressions. The Majorana-stellar representation furnishes a common geometric platform on which both the operational measure and the uncertainty products can be analyzed. For spin-1, this representation yields a three-dimensional Euclidean-like visualization of the Hilbert space in which, states lying on a plane exhibit maximum uncertainty for the observable along the perpendicular direction; simultaneous optimization across all KCBS contexts singles out a unique state on the symmetry axis. Notably, states achieving the optimal sum of uncertainty products exhibit vanishing operational contextuality, while states with substantial operational contextuality satisfy a nontrivial Robertson bound -- the two extremes are achieved by distinct quantum states.

quant-ph↗

arXiv2024

Group Theoretical Classification of SIC-POVMs

The Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) are known to exist in all dimensions $\leq 151$ and few higher dimensions as high as $1155$. All known solutions with the exception of the Hoggar solutions are covariant with respect to the Weyl-Heisenberg group and in the case of dimension 3 it has been proven that all SIC-POVMs are Weyl-Heisenberg group covariant. In this work, we introduce two functions with which SIC-POVM Gram matrices can be generated without the group covariance constraint. We show analytically that the SIC-POVM Gram matrices exist on critical points of surfaces formed by the two functions on a subspace of symmetric matrices and we show numerically that in dimensions 4 to 7, all SIC-POVM Gram matrices lie in disjoint solution "islands". We generate $O(10^6)$ and $O(10^5)$ Gram matrices in dimensions 4 and 5, respectively and $O(10^2)$ Gram matrices in dimensions 6 and 7. For every Gram matrix obtained, we generate the symmetry groups and show that all symmetry groups contain a subgroup of $3n^2$ elements. The elements of the subgroup correspond to the Weyl-Heisenberg group matrices and the order-3 unitaries that generate them. All constructed Gram matrices have a unique generating set. Using this fact, we generate permutation matrices to map the Gram matrices to known Weyl-Heisenberg group covariant solutions. In dimensions 4 and 5, the absence of a solution with a smaller symmetry, strongly suggests that non-group covariant SIC-POVMs cannot be constructed.

quant-ph↗

arXiv2023

The Degree of Quantum Contextuality in terms of Concurrence for the KCBS Scenario

Quantum contextuality is the key concept which explains the fact that the result of a measurement is not independent of the context in which it is found. It is observed to be an intrinsic feature, i.e., neither entanglement nor spatial separation is required. In this work, we revisit the previous studies which state that entanglement is an intrinsic property called self-entanglement. Using this fact, we explicitly show the correlation between quantum contextuality and concurrence in the KCBS scenario, which is the simplest approach to observing contextuality. We also derive the equation for the maximal violation of the KCBS scenario for a given concurrence and find the linear relation between them. Using this relation, we also show how the maximal violations of the KCBS and CHSH inequalities are related for an arbitrary entanglement. Moreover, we discuss the special cases of maximal entanglement, and non-entanglement for which we have found a lower local bound.

quant-ph↗

arXiv2022

Witnessing superpositions of causal orders before the process is completed

The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single point in time? Can we adapt the current formalisms to situations where the order of quantum operations is coherently or incoherently superposed? If so, what are the relations between the state at a given time and the uncertainty in the order of events before and after it? Establishing the relationship between two-state vector formalism and pseudo-density operators, we introduce the notion of a single-time pseudo-state. The tomographic construction of single-time pseudo-states is possible by ideal or weak measurements. We demonstrate that the eigenspectrum obtained from weak measurements enables us to discriminate between some coherent and incoherent superpositions of causal orders in pre- and post-selected systems before the process is completed. Finally, we discuss some possible experimental realizations in existing photonic setups.

quant-ph↗

arXiv2020

Retrit States Violating the KCBS Inequality and Necessary Conditions for Maximal Contextuality

Since violations of inequalities implied by non-contextual and local hidden variable theories are observed, it is essential to determine the set of (non-)contextual states. Along this direction, one should determine the conditions under which quantum contextuality is observed. It is also important to determine how one can find maximally contextual qutrits. In this work, we revisit the Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) scenario where we observe a five-measurement state-dependent contextuality. We investigate possible symmetries of the KCBS pentagram, i.e., the conservation of the contextual characteristic of a qutrit-system. For this purpose, the KCBS operator including five cyclic measurements is rotated around the Z-axis. We then check a set of rotation angles to determine the contextuality and non-contextuality regions for the eigenstates of the spin-1 operator for an arbitrary rotation. We perform the same operation for the homogeneous linear combination of the eigenstates with spin values +1 and -1. More generally, we work on the real subgroup of the three dimensional Hilbert space to determine the set of (non-)contextual states under certain rotations in the physical Euclidean space $\mathbb{E}^3$. Finally, we show data on Euler rotation angles for which maximally contextual retrits (qutrits of the real Hilbert space) are found, and derive mathematical relations through data analysis between Euler angles and qutrit states parameterized with spherical coordinates.

quant-ph↗

arXiv2020

Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

We have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of $N$ MUBs. Our result is valid for any state when $N$ is $d+1$, where $d$ is the dimension of the related system. We provide a quantitative criterion for the extendibilty of MUBs. In addition, we have applied our result to the mutual information of $d+1$ observables conditioned with a classical memory.

quant-ph↗

arXiv2017

Magic informationally complete POVMs with permutations

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation [M. Planat and Rukhsan-Ul-Haq, Preprint 1701.06443]. We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such IC-POVMs, investigated in dimensions $2$ to $12$, exhibit simple finite geometries in their projector products and, for dimensions $4$ and $8$ and $9$, relate to two-qubit, three-qubit and two-qutrit contextuality.

quant-ph↗

arXiv2010

Stability of Flip and Exchange Symmetric Entangled State Classes under Invertible Local Operations

Flip and exchange symmetric (FES) many-qubit states, which can be obtained from a state with the same symmetries by means of invertible local operations (ILO), constitute a one-parameter family of curves in the Hilbert space. Eigenstates of FES ILOs correspond to vectors that cannot be transformed to other FES states. This means equivalence classes of states under ILO can be determined in a systematic way for an arbitrary number of qubits. More important, for entangled states, at the boundaries of neighboring equivalence classes, one can show that when the fidelity between the final state after an ILO and a state of the neighboring class approaches unity, probability of success decreases to zero. Therefore, the classes are stable under ILOs.

quant-ph↗

arXiv2005

Spin Bath Decoherence of Quantum Entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two initially violates the inequality at early times.

quant-ph↗

arXiv2003

Quantum Phase in Nanoscopic Superconductors

Using the pseudospin representation and the SU(2) phase operators we introduce a complex parameter to characterize both infinite and finite superconducting systems. While in the bulk limit the parameter becomes identical to the conventional order parameter, in the nanoscopic limit its modulus reduces to the number parity effect parameter and its phase takes discrete values. We evaluate the Josephson coupling energy and show that in bulk superconductor it reproduces the conventional expression and in the nanoscopic limit it leads to quantized Josephson effect. Finally, we study the phase flow or dual Josephson effect in a superconductor with fixed number of electrons.

cond-mat.supr-con↗

arXiv2002

Quantum Entanglement and Order Parameter in a Paired Finite Fermi System

We study the pairing correlations in a finite Fermi system from quantum entanglement point of view. We investigate the relation between the order parameter, which has been introduced recently to describe both finite and infinite superconductors, and the concurrence. For a proper definition of the concurrence, we argue that a possible generalization of spin flip transformation is time reversal operation. While for a system with indefinite number of particles concurrence is a good measure of entanglement, for a finite system it does not distinguish between normal and superconducting states. We propose that the expectation value of the radial operator for the total pseudospin can be used to identify entanglement of pairing.

cond-mat.supr-con↗