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Preeti Parashar

Publications and source records attributed to Preeti Parashar.

At least 37 records · Page 2Linked to original sources
arXiv2013

Geometric discord and Measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's ($2\otimes 4$, $3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett etal's in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti etal and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.

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arXiv2013

Comment on "Witnessed entanglement and the geometric measure of quantum discord"

In a recent article [Phys. Rev. A 86, 024302 (2012)], the authors have derived some hierarchy relations between geometric discord and entanglement (measured by negativity and its square). We point out that these results are incorrect and give analytic counterexamples. We also discuss briefly the reason for such violations.

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arXiv2012

Entanglement is not a lower bound for geometric discord

We show that partial transposition of any $2\otimes n$ state can have at most $(n-1)$ number of negative eigenvalues. This extends a decade old result of $2\otimes 2$ case by Sanpera et al [Phys. Rev. A {\bf 58}, 826 (1998)]. We then apply this result to critically assess an important conjecture recently made in [Phys. Rev. A {\bf 84}, 052110 (2011)], namely, the (normalized) geometric discord should always be lower bounded by squared negativity. This conjecture has strengthened the common belief that measures of generic quantum correlations should be more than those of entanglement. Our analysis shows that unfortunately this is not the case and we give several counterexamples to this conjecture. All the examples considered here are in finite dimensions. Surprisingly, there are counterexamples in $2\otimes n$ for any $n>2$. Coincidentally, it appears that the $4\otimes 4$ Werner state, when seen as a $2\otimes 8$ dimensional state, also violates the conjecture. This result contributes significantly to the negative side of the current ongoing debates on the defining notion of geometric discord as a good measure of generic correlations.

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arXiv2012

Tight lower bound on geometric discord of bipartite states

We use singular value decomposition to derive a tight lower bound for geometric discord of arbitrary bipartite states. In a single shot this also leads to an upper bound of measurement-induced non locality which in turn yields that for Werner and isotropic states the two measures coincide. We also emphasize that our lower bound is saturated for all $2\otimes n$ states. Using this we show that both the generalized Greenberger-Horne-Zeilinger and $W$ states of $N$ qubits satisfy monogamy of geometric discord. Indeed, the same holds for all $N$-qubit pure states which are equivalent to $W$ states under stochastic local operations and classical communication. We show by giving an example that not all pure states of four or higher qubits satisfy monogamy.

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arXiv2011

Optimal reducibility of all Stochastic Local Operation and Classical Communication equivalent W states

We show that all multipartite pure states that are SLOCC equivalent to the $N$-qubit $W$ state, can be uniquely determined (among arbitrary states) from their bipartite marginals. We also prove that only $(N-1)$ of the bipartite marginals are sufficient and this is also the optimal number. Thus, contrary to the $GHZ$ class, $W$-type states preserve their reducibility under SLOCC. We also study the optimal reducibility of some larger classes of states. The generic Dicke states $|GD_N^\ell\ran$ are shown to be optimally determined by their ($\ell+1$)-partite marginals. The class of `$G$' states (superposition of $W$ and $\bar{W}$) are shown to be optimally determined by just two $(N-2)$-partite marginals.

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arXiv2011

Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states

We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two $N$-qubit canonical orthonormal Greenberger-Horne-Zeilinger ($GHZ$) states and the same for two $W$ states. In course of characterizing all kinds of nonclassical correlations, explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the $GHZ$ state, the closest separable state to the $W$ state is not classical. Therefore, in this case the discord is different from the relative entropy of entanglement. We conjecture that the discord for the $N$-qubit $W$ state is $\log_2N$.

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arXiv2009

Reducible Correlations in Dicke States

We apply a simple observation to show that the generalized Dicke states can be determined from their reduced subsystems. In this framework, it is sufficient to calculate the expression for only the diagonal elements of the reudced density matrices in terms of the state coefficients. We prove that the correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to $2\ell$-partite level. Application to the Quantum Marginal Problem is also discussed.

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arXiv2009

Comment on "Groverian Entanglement Measure and Evolution of Entanglement in Search Algorithm for n(= 3, 5)-Qubit Systems with Real Coefficients" (Volume 6, Number 4, August 2007), by Arti Chamoli and C. M. Bhandari

We point out that the main results-the analytic expressions for the Groverian Measure of Entanglement, in the above mentioned paper are erroneous. The technical mistake of the paper is discussed. It is shown by an explicit example that the formula for calculating the Groverian measure yields G(|ψ>) = 0 for some entangled states.

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arXiv2009

N-Qubit W States are Determined by their Bipartite Marginals

We prove that the most general W class of N-qubit states are uniquely determined among arbitrary states (pure or mixed) by just their bipartite reduced density matrices. Moreover, if we consider only pure states, then (N-1) of them are shown to be sufficient.

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arXiv2008

Constant rotation of two-qubit equally entangled pure states by local quantum operations

We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled two-qubit pure states by the same but arbitrary amount. It is shown that all two-qubit maximally entangled states can be rotated through the same but arbitrary amount by local unitary operators. But there is no local unitary operator which can rotate all equally entangled non-maximally entangled states by the same amount, unless it is unity. We have found the optimal sets of equally entangled non-maximally entangled states which can be rotated by the same but arbitrary amount via local unitary operators $W_1 \otimes W_2$, where at most one these two operators can be identity. In particular, when $W_1 = W_2 = (i/\sqrt{2})(σ_x + σ_y)$, we get the local quantum NOT operation. Interestingly, when we apply the one-sided local depolarizing map, we can rotate all equally entangled two-qubit pure states through the same amount. We extend our result for the case of three-qubit maximally entangled state.

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arXiv2007

Equal Superposition Transformations and Quantum Random Walks

The largest ensemble of qubits which satisfy the general transformation of equal superposition is obtained by different methods, namely, linearity, no-superluminal signalling and non-increase of entanglement under LOCC. We also consider the associated quantum random walk and show that all unitary balanced coins give the same asymmetric spatial probability distribution. It is further illustrated that unbalanced coins, upon appropriate superposition, lead to new unbiased walks which have no classical analogues.

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arXiv2006

On the non-existence of a universal Hadamard gate

We establish the non-existence of a universal Hadamard gate for arbitrary unknown qubits, by considering two different principles; namely, no-superluminal signalling and non-increase of entanglement under LOCC. It is also shown that these principles are not violated if and only if the qubit states are of a special form obtained in our recent work [ IJQI (in press), quant-ph/0505068 ].

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arXiv2005

Hadamard type operations for qubits

We obtain the most general ensemble of qubits, for which it is possible to design a universal Hadamard gate. These states when geometrically represented on the Bloch sphere, give a new trajectory. We further consider some Hadamard `type' of operations and find ensembles of states for which such transformations hold. Unequal superposition of a qubit and its orthogonal complement is also investigated.

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arXiv2003

Nonlocal Properties and Local Invariants for Bipartite Systems

The nonlocal properties for a kind of generic N-dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. It is shown that two generic density matrices are locally equivalent if and only if all these invariants have equal values in these density matrices.

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arXiv2000

(1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups

All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrodinger Poisson-Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and gl(2) Lie bialgebras within the Schrodinger classification are studied. As an application, new quantum (Hopf algebra) deformations of the Schrodinger algebra, including their corresponding quantum universal R-matrices, are constructed.

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arXiv1999

Two-photon algebra deformations

In order to obtain a classification of all possible quantum deformations of the two-photon algebra $h_6$, we introduce its corresponding general Lie bialgebra, which is a coboundary one. Two non-standard quantum deformations of $h_6$, together with their associated quantum universal R-matrix, are presented; each of them contains either a quantum harmonic oscillator subalgebra or a quantum gl(2) subalgebra. One-boson representations for these quantum two-photon algebras are derived and translated into Fock--Bargmann realizations. In this way, a systematic study of `deformed' states of light in quantum optics can be developed.

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arXiv1999

Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits

Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means of a contraction procedure. New quantum deformations of $gl(2)$ together with their associated quantum $R$-matrices are obtained and other known quantizations are recovered and classified. Several connections with integrable models are outlined.

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