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Pramod S. Joag

Publications and source records attributed to Pramod S. Joag.

15 recordsLinked to original sources
arXiv2024

Multipartite Generalization of Geometric measure of Discord

Radhakrishnan et.al [Phys. Rev. Lett. 124, 110401 (2020)] proposed a generalization of quantum discord to multipartite systems, which is consistency with the conventional definition of discord in bipartite systems and derived explicit formulae for any states. These results are significant in capturing quantum correlations for multi-qubit systems. We propose a generalization of geometric measure of multipartite quantum discord in the same manner. We find generic forms of the generalization of geometric measure of quantum discord in a general N-partite quantum state. Further, we obtain computable exact formulas for the generalization of geometric measure of quantum discord in an N-qubit quantum state, which include the results obtained in [arXiv:2104.12344].

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arXiv2013

Measurement-Induced Nonlocality in an $n$-partite quantum state

We generalize the concept of measurement-induced non-locality (MiN) to $n$-partite quantum states. We get exact analytical expressions for MiN in an $n$-partite pure and $n$-qubit mixed state. We obtain the conditions under which MiN equals geometric quantum discord in an $n$-partite pure state and an $n$-qubit mixed state.

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arXiv2012

Geometric measure of quantum discord and total quantum correlations in a N-partite quantum state

Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. \textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105,190502 (2010)] who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu [Phys. Rev. A \textbf{82}, 034302 (2010)] introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in a N-qubit quantum state. The exact formulas for the $N$-qubit quantum state are experimentally implementable.

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arXiv2012

Tight lower bound to the geometric measure of quantum discord

Dakic, Vedral and Brukner [Physical Review Letters \tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state which dominates that obtained by S.Luo and S.Fu.

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arXiv2011

Simulation of a Partially Entangled Two Qubit State Correlation with one PR-Box and one M-box

We present a protocol to simulate the quantum correlation implied by non maximally entangled two qubit states, in the worst case scenario. This protocol makes a single use of PR-box and a single use of Millionaire box (M-box). To the best of our knowledge, the resources used in this protocol are weaker than those used in previous protocols and are minimal in the worst case scenario.

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arXiv2010

Thermal quantum and classical correlations in two qubit XX model in a nonuniform external magnetic field

We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case (B1 = -B2), we find that QD and CC are equal for all values of (B1 = -B2) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B1 and B2. Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.

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arXiv2010

Multipartite entanglement in fermionic systems via a geometric measure

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 fermions distributed over 2L modes (single particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single particle states. This entanglement measure is defined for a given partition of 2L modes containing m >= 2 subsets. Thus this measure applies to m <= 2L partite fermionic system where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitaries corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems. To the best of our knowledge, there is no usable entanglement measure of m > 3 partite fermionic systems in the literature, so that this is the first measure of multipartite entanglement for fermionic systems going beyond the bipartite and tripartite cases.

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arXiv2010

Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach

We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334 (2008)). Our procedure reproduces the earlier results (PRL \textbf{87}, 137901 (2001)). The geometric method has the distinct advantage that it gives an experimental way to monitor the process of optimizing entanglement production.

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arXiv2010

Bound on Hardy's non-locality from the principle of Information Causality

Recently,the principle of nonviolation of information causality [Nature 461,1101 (2009)], has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two qubit systems, in the context of generalised probability theory, restricted by the principle of nonviolation of information causality. Applying, a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics,but still much less than what the nosignaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy's argument) in this context.

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arXiv2009

An Experimentally accessible geometric measure for entanglement in $N$-qudit pure states

We present a multipartite entanglement measure for $N$-qudit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for important class of $N$-qutrit pure states, namely general GHZ states. We prove that this measure possesses almost all the properties expected of a good entanglement measure, including monotonicity. Finally, we extend this measure to $N$-qudit mixed states via convex roof construction and establish its various properties, including its monotonicity.

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arXiv2008

Simulation of partial entanglement with one cbit and one M-box

We present a protocol to simulate the correlations implied by nonmaximally entangled two qubit states. We extend this protocol to simulate the non-local part of these correlations. These protocols use single cbit communication and a single use of Millionaire box (M-box). To the best of our knowledge, these resources are weaker than those used in previous protocols using classical communication.

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arXiv2008

An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states

We present a multipartite entanglement measure for $N$-qubit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for several important classes of $N$-qubit pure states such as GHZ states, W states and their superpositions. We compute this measure for interesting applications like one dimensional Heisenberg antiferromagnet. We use this measure to follow the entanglement dynamics of Grover's algorithm. We prove that this measure possesses almost all the properties expected of a good entanglement measure, including monotonicity. Finally, we extend this measure to $N$-qubit mixed states via convex roof construction and establish its various properties, including its monotonicity. We also introduce a related measure which has all properties of the above measure and is also additive.

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arXiv2008

Separability Criterion for multipartite quantum states based on the Bloch representation of density matrices

We give a new separability criterion, a necessary condition for separability of $N$-partite quantum states. The criterion is based on the Bloch representation of a $N$-partite quantum state and makes use of multilinear algebra, in particular, the matrization of tensors. Our criterion applies to {\it arbitrary} $N$-partite quantum states in $\mathcal{H}=\mathcal{H}^{d_1}\otimes \mathcal{H}^{d_2} \otimes ... \otimes \mathcal{H}^{d_N}.$ The criterion can test whether a $N$-partite state is entangled and can be applied to different partitions of the $N$-partite system. We provide examples that show the ability of this criterion to detect entanglement. We show that this criterion can detect bound entangled states. We prove a sufficiency condition for separability of a 3-partite state, straightforwardly generalizable to the case $N > 3,$ under certain condition. We also give a necessary and sufficient condition for separability of a class of $N$-qubit states which includes $N$-qubit PPT states.

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arXiv2007

Simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements

In a recent paper [A. Ahanj et al., quant-ph/0603053], we gave a classical protocol to simulate quantum correlations corresponding to the spin $s$ singlet state for the infinite sequence of spins satisfying $2s+1 = 2^{n}$. In the present paper, we have generalized this result by giving a classical protocol to exactly simulate quantum correlations implied by the spin-$s$ singlet state corresponding to all integer as well as half-integer spin values $s$. The class of measurements we consider here are only those corresponding to spin observables, as has been done in the above-mentioned paper. The required amount of communication is found to be $\lceil {\rm log}_{2} (s + 1) \rceil$ in the worst case scenario, where $\lceil x \rceil$ is the least integer greater than or equal to $x$.

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