arXiv subjects

S. Shelly Sharma

Publications and source records attributed to S. Shelly Sharma.

At least 19 recordsLinked to original sources

arXiv2021

Beyond the entanglement of qubit pair in a mixed state

Given a multipartite quantum system that consists of two-level particles (qubits), one may or may not have access to all the subsystems. What can we know about the entanglement of the multiqubit system and residual correlations beyond two-tangle if we have access only to two-qubits at a time? Algebraic analysis of two-qubit states yields monogamy constraints on distribution of entanglement between sub-systems of an N-qubit state and criterion to determine if the state has multipartite entanglement. Monogamy constraints, reported in this letter, are relations between well known entanglement measures such as one-tangle, two-tangles and three-tangles of an N-qubit pure state.

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arXiv2021

Monogamy constraints on entanglement of four-qubit pure states

We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal state $ρ$ of a four qubit pure state $\left\vert Ψ_{4}\right\rangle $, the non-Hermitian matrix $ρ\widetildeρ$ where $\widetildeρ$ $=\left( σ_{y} \otimesσ_{y}\right) ρ^{\ast}\left( σ_{y}\otimesσ_{y}\right) $, contains information not only about the entanglement properties of the two-qubits in state $ρ$ but also about three tangles involving the selected pair as well as four-way correlations of the pair of qubits in $\left\vert Ψ_{4}\right\rangle $. To extract information about tangles of a four-qubit state $\left\vert Ψ_{4}\right\rangle $, the coefficients in the characteristic polynomial of matrix $ρ\widetildeρ$ are analytically expressed in terms of $2\times2$ matrices of state coefficients. Four-tangles distinguish between different types of entangled four-qubit pure states.

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arXiv2018

On Monogamy of four qubit entanglement

Our main result is a monogamy inequality satisfied by the entanglement of a focus qubit (one-tangle) in a four-qubit pure state and entanglement of subsystems. Analytical relations between three-tangles of three-qubit marginal states, two-tangles of two-qubit marginal states and unitary invariants of four-qubit pure state are used to obtain the inequality. The contribution of three-tangle to one-tangle is found to be half of that suggested by a simple extension of entanglement monogamy relation for three qubits. On the other hand, an additional contribution due to a two-qubit invariant which is a function of three-way correlations is found. We also show that four-qubit monogamy inequality conjecture of ref. [PRL 113, 110501 (2014)] in which three-tangles are raised to the power (3/2), does not estimate the residual correlations, correctly. A lower bound on residual four-qubit correlations is obtained.

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arXiv2017

Upper bound on three tangles of reduced states of four-qubit pure states

Closed formulae for upper bound on three tangles of three-qubit reduced states in terms of three-qubit invariant polynomials of pure four-qubit states are obtained. Our results offer tighter constraints on total three-way entanglement of a given qubit with the rest of the system than those used in ref. [PRL 113, 110501 (2014), PRL 116, 049902(E) (2016)] to verify monogamy of four-qubit quantum entanglement.

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arXiv2016

Sequential generation of Polynomial Invariants and N-body non-local correlations

We report an inductive process that allows for a sequential construction of polynomial invariants of state coefficients for multipartite quantum states. The starting point can be a physically meaningful invariant of a smaller part of the system. The process is applied to construct a chain of invariants that quantify GHZ state like non-local N-way correlations in an N qubit pure state and the sum of N-way and (N-1)-way correlations. Analytic expressions for four and three-way correlation quantifiers for four qubits, as well as, five-way and four-way correlation quantifiers for a five qubit pure state are given.

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arXiv2013

Genuine Four Tangle for Four Qubit States

We report a four qubit polynomial invariant that quantifies genuine four-body correlations. The four qubit invariants are obtained from transformation properties of three qubit invariants under a local unitary on the fourth qubit.

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arXiv2013

Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts

Local unitary invariance and the notion of negativity fonts are used as the principle tools to construct four qubit invariants of degree 8, 12, and 24. A degree 8 polynomial invariant that is non-zero on pure four qubit states with four-body correlations and zero on all other states, is identified. Classification of four qubit states into seven major classes, using criterion based on the nature of correlations, is discussed.

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arXiv2012

Classification of Multipartite Entanglement via Negativity Fonts

Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to conceptually multipartite underlying structures in a state - the negativity fonts. If K-way negativity fonts with non zero determinants exist, then selective partial transposition of a pure state, involving K of the N qubits (K leq N) yields an operator with negative eigevalues, identifying K-body correlations in the state. Expansion of GPT interms of K-way partially transposed (KPT) operators reveals the nature of intricate intrinsic correlations in the state. Classification criteria for multipartite entangled states, based on underlying structure of global partial transpose of canonical state, are proposed. Number of N-partite entanglement types for an N qubit system is found to be 2^{N-1}-N+2, while the number of major entanglement classes is 2^{N-1}-1. Major classes for three and four qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical state.

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arXiv2011

Entanglement generation and transfer between remote atomic qubits interacting with squeezed field

A pair of two level atoms A1A2, prepared either in a separable state or in an entangled state, interacts with a single mode of two mode squeezed cavity field while a third atomic qubit B interacts with the second mode of the squeezed field in a remote cavity. We analyze, numerically, the generation, sudden death and revival of three qubit entanglement as a function of initial entanglement of qubits A1A2 and degree of squeezing of electromagnetic field. Global negativity of partially transposed state operator is used to quantify the entanglement of three atom state. It is found that the initial entanglement of two mode field as well as that of the pair A1A2, both, contribute to three atom entanglement. A maximally entangled single excitation Bell pair in first cavity and two mode field with squeeze parameter s=0.64 are the initial conditions that optimize the peak value of three qubit mixed state entanglement. A smaller value of s=0.4 under similar conditions is found to generate a three qubit mixed state with comparable entanglement dynamics free from entanglement sudden death.

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arXiv2011

Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States

Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N- qubit state and linear entropy of reduced single qubit state yields an expression for global negativity in terms of determinants of negativity fonts. Transformation equations for determinants of negativity fonts under local unitaries (LU's) are useful to construct LU invariants such as degree four and degree six invariants for four qubit states. The difference of squared negativity and N-tangle is an N qubit invariant which contains information on entanglement of the state caused by quantum coherences that are not annihilated by removing a single qubit. Four qubit invariants that detect the entanglement of specific parts in a four qubit state are expressed in terms of three qubit subsystem invariants. Numerical values of invariants bring out distinct features of several four qubit states which have been proposed to be the maximally entangled four qubit states.

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arXiv2010

Local Unitary Invariants for N-qubit Pure State

We obtain local unitary invariant polynomials for N qubit quantum state from first principles. A basic unit of entanglement, referred to as negativity font, is defined as a two by two matrix of probability amplitudes that determines the negative eigen value of a four by four submatrix of partially transposed state operator. Transformation properties of determinants of negativity fonts under local unitary (LU) transformations are exploited to obtain multi qubit invariants written in terms of such determinants.

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arXiv2009

Four-tangle for pure states

An expression for four-tangle is obtained by examining the negativity fonts present in a four-way partial transpose under local unitary operations. An alternate derivation of three tangle is also given.

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arXiv2009

Partial K-way Negativities of Pure Four qubit Entangled States

It has been shown by Versraete et. al [F. Versraete, J. Dehaene, B. De Moor, and H. Verschelde, Phys. Rev. A65, 052112 (2002)] that by stochastic local operations and classical communication (SLOCC), a pure state of four qubits can be transformed to a state belonging to one of a set of nine families of states. By using selective partial transposition, we construct partial K-way negativities to measure the genuine 4-partite, tripartite, and bi-partite entanglement of single copy states belonging to the nine families of four qubit states. Partial K-way negativities are polynomial functions of local invariants characterizing each family of states as such entanglement monotones.

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arXiv2009

Generation of field mediated three qubit entangled state shared by Alice and Bob

A scheme to generate shared tripartite entangled states, with two-trapped atoms in a cavity held by Alice (qubits A1 and A2) entangled to a single trapped atom in a remote lab owned by Bob (B), is proposed. The entanglement is generated through interaction of trapped atoms with two mode squeezed light shared by the two cavities. The proposed scheme is an extension of the proposal of ref. [W. Son, M. S. Kim, J. Lee, and D. Ahn, J. Mod. Opt. 49, 1739 (2002)], where the possibility of entangling two remote qubits using a bipartite continuous variable state was examined. While the global negativity detects the free entanglement of the three atom mixed state, the bound entanglement is detected by the negativity calculated from pure state decomposition of the state operator. The partial negativities calculated by selective partial transposition of the three atom mixed state detect the pairwise entanglement of qubit pairs A1B, A2B, and A1A2. The entanglement of three atoms is found to be W-like, no GHZ like quantum correlations being generated.

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arXiv2008

Multipartite entanglement of three trapped ions in a cavity and W- State generation

A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with red sideband tuned single mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating three ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 $μ$ sec. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by appropriate choice of initial state phonon number. The ionic qubits in W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial $K-$way negativities (K=2 to 4) are obtained to study the evolution of entanglement distribution as a function of interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of interaction parameter, the three ions and photon-phonon system are found to have four partite entanglement, generated by 2-way and 3-way correlations.

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arXiv2008

Partial K-way negativities and three tangle for three qubit states

We obtain, analytically, the global negativity, partial $K-$way negativities (K=2, 3), Wooter's tangle and three tangle for the generic three qubit canonical state. It is found that the product of global negativity and partial three way negativity is equal to three tangle, while the partial two way negativity is related to tangle of qubit pairs. We also calculate similar quantities for the state canonical to a single parameter (0<q<1) pure state which is a linear combination of a GHZ state and a W state. In this case for q=0.62685, the state has zero three tangle and zero three-way negativity, having only W-like entanglement. The difference between the product of global and partial three way negativity and three tangle for a given state is a quantitative measure of two qubit coherences transformed by unitary transformations on canonical state into three qubit coherences. The global negativity and partial K-way negativities, obtained by selective partial transpositions on multi-qubit state operator, satisfy inequalities which for three qubits are equivalent to CKW (Coffman-Kundu-Wootter) inequality.

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arXiv2008

Quantum coherences, K-way negativities and multipartite entanglement

A characterization of N-partite states, based on K-way (K = 2 to N) negativities, is proposed. The K-way partial transpose with respect to a subsystem is defined so as to shift the focus to K-way coherences instead of K subsystems of the composite system. For an N-partite system the fraction of K-way negativity, contributing to global negativity, is obtained. The entanglement measures for a given state $ρ$ are identified as the partial K-way negativities of the corresponding canonical state.

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arXiv2007

The K-way negativities as entanglement measures

A classification of N-partite states, based on K-way negativities (K=2 to N), is proposed. The K-way partial transpose with respect to a subsystem is defined so as to shift the focus to K-way coherences instead of K subsystems of the composite system. For an N-partite system, the fraction of K-way negativity contributing to global negativity, is obtained. After minimizing K-way negativities through local unitary qubit rotations, a combined analysis of 2-way, 3-way and global negativities is shown to provide distinct measures of genuine tripartite, W-state like and bipartite entanglement, for three qubit composite system. To illustrate the point, entanglement of three qubit GHZ class states, W-class states, three boson state and noisy states is analysed. While genuine N-partite entanglement of a composite system is generated by N-way coherences, N-partite entanglement in general can be present due to (K<N)-way coherences as well.

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