arXiv subjects

Seyed Javad Akhtarshenas

Publications and source records attributed to Seyed Javad Akhtarshenas.

17 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 $1/3\leμ\le 1/2$ where $μ=\sum_{k=0}^{2}q_k^2$. 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 $μ$, 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 ...

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arXiv2024

Optimal quantum speed for mixed states

The question of how fast a quantum state can evolve is considered. Using the definition of squared speed based on the Euclidean distance given in [Phys. Rev. Research, {\bf 2}, 033127 (2019)], we present a systematic framework to obtain the optimal speed of a $d$-dimensional system evolved unitarily under a time-independent Hamiltonian. Among the set of mixed quantum states having the same purity, the optimal state is obtained in terms of its purity parameter. We show that for an arbitrary $d$, the optimal state is represented by a $X$-state with an additional property of being symmetric with respect to the secondary diagonal. For sufficiently low purities for which the purity exceeds the purity of maximally mixed state $\Id/d$ by at most $2/d^2$, the only nonzero off-diagonal entry of the optimal state is $\varrho_{1d}$, corresponding to the transition amplitude between two energy eigenstates with minimum and maximum eigenvalues, respectively. For larger purities, however, whether or not the other secondary diameter entries $\varrho_{i,d-i+1}$ take nonzero values depends on their relative energy gaps $|E_{d-i+1}-E_{i}|$. The effects of coherence and entanglement, with respect to the energy basis, are also examined and found that for optimal states both resources are monotonic functions of purity, so they can cause speed up quantum evolution leading to a smaller quantum speed limit. Our results show that although the coherence of the states is responsible for the speed of evolution, only the coherence caused by some off-diagonal entries located on the secondary diagonal play a role in the fastest states.

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arXiv2024

Measurement sharpness and disturbance tradeoff

Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement model, complicating the puzzle of information-disturbance. Two distinct questions are then in order. Firstly, what is the minimum disturbance a measurement may induce? Secondly, when a fixed disturbance occurs, how informative is the possible measurement in the best-case scenario? Here, we propose various approaches to tackle these questions and provide explicit solutions for the set of unbiased binary qubit measurements and postmeasurement state spaces that are equivalent to the image of a unital qubit channel. In particular, we show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces as well as the sharpness and quantum resources preserved in the postmeasurement states in terms of coherence and discord-like correlation once the measurement is applied locally.

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arXiv2021

Mutually unbiased measurements with arbitrary purity

Mutually unbiased measurements are a generalization of mutually unbiased bases in which the measurement operators need not to be rank one projectors. In a $d$-dimension space, the purity of measurement elements ranges from $1/d$ for the measurement operators corresponding to maximally mixed states to $1$ for the rank one projectors. In this contribution, we provide a class of MUM that encompasses the full range of purity. Similar to the MUB in which the operators corresponding to different outcomes of the same measurement commute mutually, our class of MUM possesses this sense of compatibility within each measurement. This makes the provided class more similar to the MUB, so that the main difference between them and MUB is due to the purity of the measurement operators. The spectra of these MUMs provides a way to construct a class of $d$-dimensional orthogonal matrices which leave the vector of equal components invariant. Based on this property, and by using the MUM-based entanglement witnesses, we investigate the role of purity to detect entanglement of bipartite states.

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arXiv2018

Quantum Fisher information matrix for unitary processes: closed relation for $SU(2)$

Quantum Fisher information plays a central role in the field of quantum metrology. In this paper we study the problem of quantum Fisher information of unitary processes. Associated to each parameter $θ_i$ of unitary process $U(\boldsymbolθ)$, there exists a unique Hermitian matrix $M_{θ_i}=i(U^\dagger\partial_{θ_i} U)$. Except for some simple cases, such as when the parameter under estimation is an overall multiplicative factor in the Hamiltonian, calculation of these matrices is not an easy task to treat even for estimating a single parameter of qubit systems. Using the Bloch vector $\boldsymbol{m}_{θ_i}$, corresponding to each matrix $M_{θ_i}$, we find a closed relation for the quantum Fisher information matrix of the $SU(2)$ processes for an arbitrary number of estimation parameters and an arbitrary initial state. We extend our results and present an explicit relation for each vector $\boldsymbol{m}_{θ_i}$ for a general Hamiltonian with arbitrary parametrization. We illustrate our results by obtaining the quantum Fisher information matrix of the so-called angle-axis parameters of a general $SU(2)$ process. Using a linear transformation between two different parameter spaces of a unitary process, we provide a way to move from quantum Fisher information of a unitary process in a given parametrization to the one of the other parametrization. Knowing this linear transformation enables one to calculate the quantum Fisher information of a composite unitary process, i.e. a unitary process resulted from successive action of some simple unitary processes. We apply this method for a spin-half system and obtain the quantum Fisher matrix of the coset parameters in terms of the one of the angle-axis parameters.

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arXiv2018

Measuring quantum discord using the most distinguishable steered states

Any two-qubit state can be represented, geometrically, as an ellipsoid with a certain size and a center located within the Bloch sphere of one of the qubits. Points of this ellipsoid represent the post-measurement states when the other qubit is measured. Based on the most demolition concept in the definition of quantum discord, we study the amount of demolition when the two post-measurement states, represented as two points on the steering ellipsoid, have the most distinguishability. We use trace distance as a measure of distinguishability and obtain the maximum distinguishability for some classes of states, analytically. Using the optimum measurement that gives the most distinguishable steered states, we extract quantum correlation of the state and compare the result with the quantum discord. It is shown that there are some important classes of states for which the most demolition happens exactly at the most distinguished steered points. Correlations gathered from the most distinguished post-measurement states provide a faithful and tight upper bound touching the quantum discord in most of the cases.

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arXiv2018

Quantumness of quantum channels

Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent to which quantum coherence is diminished depends both on the channel and the incoherent basis. Motivated by this, we propose a measure of nonclassicality of a quantum channel as the average quantum coherence of the state space after the channel acts on, minimized over all orthonormal basis sets of the state space. Utilizing the squared $l_1$-norm of coherence for the qubit channels, the minimization can be treated analytically and the proposed measure takes a closed form of expression. If we allow the channels to act locally on a maximally entangled state, the quantum correlation is diminished making the states more classical. We show that the extent to which quantum correlation is preserved under local action of the channel cannot exceed the quantumness of the underlying channel. We further apply our measure to the quantum teleportation protocol and show that a nonzero quantumness for the underlying channel provides a necessary condition to overcome the best classical protocols.

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arXiv2018

Parametrization of quantum states and the quantum state discrimination problem

A discrimination problem consists of $N$ linearly independent pure quantum states $Φ=\{\ket{ϕ_i}\}$ and the corresponding occurrence probabilities $η=\{η_i\}$. To any such problem we associate, up to a permutation over the probabilities $\{η_i\}$, a unique pair of density matrices $\boldsymbol{ρ_{_{T}}}$ and $\boldsymbol{η_{p}}$ defined on the $N$-dimensional Hilbert space $\mathcal{H}_N$. The first one, $\boldsymbol{ρ_{_{T}}}$, provides a new parametrization of a generic full-rank density matrix in terms of the parameters of the discrimination problem, i.e. the mutual overlaps $γ_{ij}=\bra{ϕ_i}ϕ_j\rangle$ and the occurrence probabilities $\{η_i\}$. The second one is defined as a diagonal density matrix $\boldsymbol{η_p}$ with the diagonal entries given by the probabilities $\{η_i\}$ with the ordering induced by the permutation $p$ of the probabilities. $\boldsymbol{ρ_{_{T}}}$ and $\boldsymbol{η_{p}}$ capture information about the quantum and classical versions of the discrimination problem, respectively. In this sense, when the set $Φ$ can be discriminated unambiguously with probability one, i.e. when the states to be discriminated are mutually orthogonal and can be distinguished by a classical observer, then $\boldsymbol{ρ_{_{T}}}\rightarrow \boldsymbol{η_{p}}$. Moreover, if the set lacks its independency and cannot be discriminated anymore the distinguishability of the pair, measured by the fidelity $F(\boldsymbol{ρ_{_{T}}}, \boldsymbol{η_{p}})$, becomes minimum. This enables one to associate to each discrimination problem a measure of discriminability defined by the fidelity $F(\boldsymbol{ρ_{_{T}}}, \boldsymbol{η_{p}})$. This quantity, has the advantage of being easy to calculate and in this respect it can find useful applications in estimating the extent to which the set is discriminable.

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arXiv2017

Reexamination of strong subadditivity: A quantum-correlation approach

The strong subadditivity inequality of von Neumann entropy relates the entropy of subsystems of a tripartite state $ρ_{ABC}$ to that of the composite system. Here, we define $\boldsymbol{T}^{(a)}(ρ_{ABC})$ as the extent to which $ρ_{ABC}$ fails to satisfy the strong subadditivity inequality $S(ρ_{B})+S(ρ_{C}) \le S(ρ_{AB})+S(ρ_{AC})$ with equality and investigate its properties. In particular, by introducing auxiliary subsystem $E$, we consider any purification $|ψ_{ABCE}\rangle$ of $ρ_{ABC}$ and formulate $\boldsymbol{T}^{(a)}(ρ_{ABC})$ as the extent to which the bipartite quantum correlations of $ρ_{AB}$ and $ρ_{AC}$, measured by entanglement of formation and quantum discord, change under the transformation $B\rightarrow BE$ and $C\rightarrow CE$. Invariance of quantum correlations of $ρ_{AB}$ and $ρ_{AC}$ under such transformation is shown to be a necessary and sufficient condition for vanishing $\boldsymbol{T}^{(a)}(ρ_{ABC})$. Our approach allows one to characterize, intuitively, the structure of states for which the strong subadditivity is saturated. Moreover, along with providing a conservation law for quantum correlations of states for which the strong subadditivity inequality is satisfied with equality, we find that such states coincides with those that the Koashi-Winter monogamy relation is saturated.

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arXiv2016

Entangled graphs: A classification of four-qubit entanglement

We use the concept of \textit{entangled graphs} with weighted edges to present a classification for four-qubit entanglement which is based neither on the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al. [Phys. Rev. A 67, (2003) 012322], are structures such that each qubit of a multi-qubit system is represented as a vertex and an edge between two vertices denotes bipartite entanglement between the corresponding qubits. Our classification is based on the use of generalized Schmidt decomposition of pure states of multi-qubit systems. We show that for every possible entangled graph one can find a pure state such that the reduced entanglement of each pair, measured by concurrence, represents the weight of the corresponding edge in the graph. We also use the concept of tripartite and quadripartite concurrences as a proper measure of global entanglement of the states. In this case a circle including the graph indicates the presence of global entanglement.

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arXiv2016

Comparison of quantum discord and fully entangled fraction of two classes of $d\otimes d^2$ states

The quantumness of a generic state is the resource of many applications in quantum information theory and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the $d\otimes d$ Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.

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arXiv2016

Revealing quantum correlation by negativity of the Wigner function

We analyze two two-mode continuous variable separable states with the same marginal states. We adopt the definition of classicality in the form of well-defined positive Wigner function describing the state and find that although the states possess positive local Wigner functions, they exhibit negative Wigner functions for the global states. Using the negativity of Wigner function as an indicator of nonclassicality, we show that despite these states possess different negativities of the Wigner function, they do not reveal this difference as phase space nonclassicalities such as negativity of the Mandel $Q$ parameter or quadrature squeezing. We then concentrate on quantum correlation of these states and show that quantum discord and local quantum uncertainty, as two well-defined measures of quantum correlation, manifest the difference between negativity of the Wigner functions. The non-Gaussianity of these states is also examined and show that the difference in behavior of their non-Gaussianity is the same as the difference between negativity of their Wigner functions. We also investigate the influence of correlation rank criterion and find that when the states can be produced locally from classical states, the Wigner functions can not reveal their quantum correlations.

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arXiv2016

Quantifying Nonclassicality of Correlations based on the Concept of Nondisruptive Local State Identification

A bipartite state is classical with respect to party $A$ if and only if party $A$ can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation measures for an arbitrary bipartite state. The measures utilize the general Schatten $p$-norm to quantify the amount of departure from the necessary and sufficient condition of classicality of correlations provided by the concept of NDLID. We show that for the case of Hilbert-Schmidt norm, i.e. $p=2$, a closed formula is available for an arbitrary bipartite state. The reliability of the proposed measures is checked from the information theoretic perspective. Also, the monotonicity behavior of these measures under LOCC is exemplified. The results reveal that for the general pure bipartite states these measures have an upper bound which is an entanglement monotone in its own right. This enables us to introduce a new measure of entanglement, for a general bipartite state, by convex roof construction. Some examples and comparison with other quantum correlation measures are also provided.

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arXiv2015

Computable Measure of Total Quantum Correlation of Multipartite Systems

Quantum discord as a measure of the quantum correlations cannot be easily computed for most of density operators. In this paper, we present a measure of the total quantum correlations that is operationally simple and can be computed effectively for an arbitrary mixed state of a multipartite system. The measure is based on the coherence vector of the party whose quantumness is investigated as well as the correlation matrix of this part with the remainder of the system. Being able to detect the quantumness of multipartite systems, such as detecting the quantum critical points in spin chains, alongside with the computability characteristic of the measure, make it a useful indicator to be exploited in the cases which are out of the scope of the other known measures.

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arXiv2010

On the concurrence of superpositions of many states

In this paper we use the \textit{concurrence vector}, as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by \textit{I-concurrence}, so that our results can be compared to those given in [Phys. Rev. A {\bf 76}, 042328 (2007)]. We obtain a tighter lower bound in the case that two superposed states are orthogonal. We also show that when the two superposed states are not necessarily orthogonal, both lower and bounds are, in general, tighter than the bounds given in terms of the I-concurrence. An extension of the results to the case with more than two states in the superpositions is also given.

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arXiv2010

Tunneling effects in a one-dimensional quantum walk

In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime of this type of noise the quantum behavior of the walker does not fade, in contrary to the coin decoherence for which the walker undergos the quantum-to-classical transition even for weak noise. Particularly, we show that the quadratic dependency of the variance on the time and also the coin-position entanglement, i.e. two important quantum aspects of the coherent quantum walk, are preserved in the presence of tunneling decoherence. Furthermore, we present an explicit expression for the probability distribution of decoherent one-dimensional quantum walk in terms of the corresponding coherent probabilities, and show that this type of decoherence smooths the probability distribution.

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arXiv2009

Decoherence in one-dimensional Quantum Walk

In this paper we study decoherence in the quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al [Phys. Rev. A {\bf 67}, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is subjected to decoherence.

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