arXiv subjects

Saman Karimi

Publications and source records attributed to Saman Karimi.

5 recordsLinked to original sources

arXiv2025

Mutually equibiased bases

In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be predicted according to a predefined probability distribution $q=(q_0,\ldots,q_{d-1})$. The notion of mutual unbiasedness, however, is preserved by requiring that the extracted information is the same for any preparation and any measurement; regardless of which state from which basis is chosen to prepare the system, the outcomes of measuring the system with respect to the other basis generate the same probability distribution. In light of this, we define the notion of \emph{mutually equibiased bases} (MEBs) such that within each basis the states are equibiased with respect to the states of the other basis and that the bases are mutually equibiased with respect to each other. For $d=2,3$, we derive a set of $d+1$ MEBs. The mutual equibiasedness imposes nontrivial constraints on the distribution $q$, leading for $d=3$ to the restriction $1/3\le\mu \le 1/2$ where $\mu=\sum_{k=0}^{2}q_k^2$. To capture the incompatibility of the measurements in MEBs, we derive an inequality for the probabilities of projective measurements in a qudit system, which yields an associated entropic uncertainty inequality. Finally, we construct a class of positive maps and their associated entanglement witnesses based on MEBs. While an entanglement witness constructed from MUBs is generally finer than one based on MEBs when both use the same number of bases, for certain values of the index $\mu$, employing a larger set of MEBs can yield a finer witness. We illustrate this behavior using isotropic states of a $3\times 3$ system. Our results reveal that not all bases in a set of $L$ MEBs can contribute to the entanglement detection. A constraint, dependent on the probability ...

quant-ph↗

arXiv2022

Couplings of order six in the gauge field strength and the second fundamental form on a D$_p$-brane at order $α'^2$

Using the assumption that the independent gauge invariant couplings on the world-volume of the non-perturbative objects in the string theory are independent of the background, we find the four and the six gauge field strength and/or the second fundamental form couplings on the world volume of a D$_p$-brane in the superstring theory at order $α'^2$ in the normalization that $F$ is dimensionless. We have found them by considering the particular background which has one circle and by imposing the corresponding T-duality constraint on the independent couplings. In particular, we find that there are 12+146 independent gauge invariant couplings at this order, and the T-duality constraint can fix 150 of them. We show that these couplings are fully consistent with the partial results in the literature. This comparison also fixes the remaining 8 couplings.

hep-th↗

arXiv2021

$α'$-corrections to DBI action via T-duality constraint

It is known that D$_p$-brane effective action at the leading order of $α'$ in flat space-time which is given by DBI action, transforms to D$_{p-1}$-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order $α'$, one may find corrections to the DBI action which include the second fundamental form $Ω$ and the covariant derivative of gauge field strength $DF$, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of $D FD F$ and $ΩΩ$ with zero, two, four and six $F$'s. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature.

hep-th↗

arXiv2020

Holographic complexity in general quadratic curvature theory of gravity

In the context of CA conjecture for holographic complexity, we study the action growth rate at late time approximation for general quadratic curvature theory of gravity. We show how the Lloyd's bound saturates for charged and neutral black hole solutions. We observe that a second singular point may modify the action growth rate to a value other than the Lloyd's bound. Moreover, we find the universal terms that appear in the divergent part of complexity from computing the bulk and joint terms on a regulated WDW patch.

hep-th↗

arXiv2014

Computable measure of the quantum correlation

A general state of an $m\otimes n$ system is a classical-quantum state if and only if its associated $A$-correlation matrix (a matrix constructed from the coherence vector of the party $A$, the correlation matrix of the state, and a function of the local coherence vector of the subsystem $B$), has rank no larger than $m-1$. Using the general Schatten $p$-norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $p$-norms and any function of the local coherence vector of the unmeasured subsystem, leading to a class of computable quantities which can be used to capture the quantumness of correlations due to the subsystem $A$. We introduce two special members of these quantifiers; The first one coincides with the tight lower bound on the geometric measure of discord, so that such lower bound fully captures the quantum correlation of a bipartite system. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord. The second quantifier has the property that it is invariant under a local and reversible operation performed on the unmeasured subsystem, so that it can be regarded as a computable well-defined measure of the quantum correlations. The approach presented in this paper provides a way to circumvent the problem with the geometric discord. We provide some examples to exemplify this measure.

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