PT
	    
	   symmetric evolution, coherence and violation of Leggett–Garg inequalities

Naikoo, Javid; Kumari, Swati; Banerjee, Subhashish; Pan, A. K.

doi:10.1088/1751-8121/ac0546

Cited by 10 publications

(7 citation statements)

References 66 publications

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“…PT-symmetric Hamiltonians have attracted wide attention due to their interesting features, and numerous studies have been performed including increase or restoration of entanglement by a local PT-symmetric Hamiltonian [12,14], protecting quantum correlations via non-hermitian operations [15], no-signaling principle violation [16,17], observing fast evolution in a PTsymmetric system [18,19] and observing critical phenomena in a PT-symmetric system [20,21]. Recently, it has been shown that quantum coherence is increased in a single-qubit system under PT-symmetric Hamiltonian and maximal quantum coherence is observed at the exceptional point [22,23]. The flow of quantum coherence of a single qubit under PT-symmetric and anti-PTsymmetric Hamiltonians has been demonstrated on an optics system [24].…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

Gautam¹,

Dorai²,

Arvind³

2022

Preprint

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In this work, we study the dynamics of quantum coherence (total coherence, global coherence and local coherence) evolving under a local PT-symmetric Hamiltonian in maximally entangled bipartite and tripartite states. Our results indicate that quantum coherence in the bipartite state oscillates in the unbroken phase regime of the PT-symmetric Hamiltonian. Interestingly, in the broken phase regime, while the global coherence decays exponentially, the local and total coherences enter a "freezing" regime where they attain a stable value over time. A similar pattern is observed for the dynamics of total and local coherences in the maximally entangled tripartite state, while the dynamics of global coherence in this state differs from that of the bipartite state. These results were experimentally validated for a maximally entangled bipartite state on a three-qubit nuclear magnetic resonance (NMR) quantum processor, with one of the qubits acting as an ancilla. The experimental results match well with the theoretical predictions, upto experimental errors.

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Section: Introductionmentioning

confidence: 99%

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

Gautam¹,

Dorai²,

Arvind³

2022

Preprint

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“…1 (Left)). Recently it has been shown that K 3 can take values upto its algebraic bound in case of a TLS undergoing non-Hermitian dynamics (PT-symmetric with fixed eigenspectrum) 20,21 and close to the exceptional point in the PT-symmetric phase 22 . Whereas we explore the non-Hermitian dynamics of a TLS across the exceptional point separating the PT-symmetric and PTbroken phases.…”

Section: Introductionmentioning

confidence: 99%

Essential role of quantum speed limit in violation of Leggett-Garg inequality across a PT-transition

V.¹,

E.²,

Paul³

et al. 2022

Preprint

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We study Leggett-Garg inequality (LGI) of a two level system (TLS) undergoing non-Hermitian dynamics governed by a non-linear Bloch equation (derived in J. Phys. A: Math. Theor. 54, 115301 (2021)) across a PT-transition. We present an algebraic identification of the parameter space for the maximum violation of LGI (in particular K3). In the PT-symmetric regime the maximum allowed value for K3 is always found to be greater than the quantum bound (Lüders bound) of 3/2 but it does not reach the algebraic maximum of K3 = 3 in general. However, in the limit where PTsymmetry breaking parameter approaches the exceptional point from the PT-symmetric side, K3 is found to asymptotically approach its algebraic maximum of 3. In contrast, the maximum value of K3 always reaches its algebraic maximum in the PT-broken phase i.e. K3 → 3. We find that (i) the speed of evolution (SOE) must reach its maximum value (in the parameter space of initial state and the time interval between successive measurements) to facilitate the value of K3 → 3, (ii) together with the constraint that its minimum value must run into SOE equals to zero during the evolution of the state. In fact we show that the minimum speed of evolution can serve as an order parameter which is finite on the PT-symmetric side and identically zero on the PT-broken side. Finally, we discuss a possible experimental realization of this dynamics by quantum measurement followed by post-selection procedure in a three level atom coupled to cavity mode undergoing a Lindbladian dynamics.

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“…Recently, using

\mathcal {PT}

‐symmetric evolution, [ 43 ] it has been shown that the quantum violation of standard LGIs in quantum theory can approach the algebraic maximum for four‐time [ 61 ] as well as three‐time LGI [ 62 ] scenarios. In ref.…”

Section: Introductionmentioning

confidence: 99%

“…In ref. [62], one of us has shown the enhancement of coherence around the exception point of

\mathcal {PT}

‐symmetric systems and its impact on the degree of violation of LGIs. Although our work is along this line, we additionally study the quantum violation of the variant of LGIs in a three‐time LG scenario.…”

Section: Introductionmentioning

confidence: 99%

Lüders Bounds of Leggett–Garg Inequalities, PT$\mathcal {PT}$‐ Symmetric Evolution and Arrow‐of‐Time

Kumari

Pan

2022

Annalen der Physik

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Leggett–Garg inequalities (LGIs) test the incompatibility between the notion of macrorealism and quantum theory. For unitary dynamics, the optimal quantum violation of a Leggett–Garg inequality is constrained by the Lüders bound. However, the LGIs do not provide the necessary and sufficient condition of macrorealism. A suitably formulated set of no‐signaling in time conditions along with the arrow‐of‐time condition provides the same. In this paper, two formulations in the three‐time Leggett–Garg scenario, are studied namely, the standard LGIs and the recently formulated variant of LGIs when the system evolves under PT‐symmetric Hamiltonian. It is first demonstrated that the quantum violations of both forms of LGIs exceed their respective Lüders bounds and can even reach their algebraic maximum. It is further shown that for the case of standard Leggett–Garg inequality, the violation of Lüders bound can be obtained when both no‐signaling in time and arrow‐of‐time conditions are violated. Interestingly, for the case of a variant of LGIs, for suitable choices of relevant parameters, the quantum violation can even be obtained when only the arrow‐of‐time is violated. However, all no‐signaling in time conditions are satisfied. Such a feature is hitherto unexplored.

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PT symmetric evolution, coherence and violation of Leggett–Garg inequalities

Cited by 10 publications

References 66 publications

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

Essential role of quantum speed limit in violation of Leggett-Garg inequality across a PT-transition

Lüders Bounds of Leggett–Garg Inequalities, PT$\mathcal {PT}$‐ Symmetric Evolution and Arrow‐of‐Time

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