Leggett-Garg inequality violations with a large ensemble of qubits

Lambert, Neill; Debnath, Kamanasish; Kockum, Anton Frisk; Knee, George C.; Munro, William J.; Nori, Franco

doi:10.1103/physreva.94.012105

Cited by 46 publications

(42 citation statements)

References 57 publications

(82 reference statements)

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“…We propose a possible quantification of intrinsic disturbance, based on the conditions in Eq. (15), and study the operations that do not increase it. We call them "free processes" or "free operations" following the terminology of resource theories (see, e.g., Ref.…”

Section: Perspectives On Incompatibility Quantification As Intrinmentioning

confidence: 99%

Leggett-Garg macrorealism and the quantum nondisturbance conditions

2019

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We investigate the relation between a refined version of Leggett and Garg conditions for macrorealism, namely the no-signaling-in-time (NSIT) conditions, and the quantum mechanical notion of nondisturbance between measurements. We show that all NSIT conditions are satisfied for any state preparation if and only if certain compatibility criteria on the state-update rules relative to the measurements, i.e. quantum instruments, are met. The systematic treatment of NSIT conditions supported by structural results on nondisturbance provides a unified framework for the discussion of the the clumsiness loophole. This extends previous approaches and allows for a tightening of the loophole via a hierarchy of tests able to disprove a larger class of macrorealist theories. Finally, we discuss perspectives for a resource theory of quantum mechanical disturbance related to violations of macrorealism.

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Section: Perspectives On Incompatibility Quantification As Intrinmentioning

confidence: 99%

Leggett-Garg macrorealism and the quantum nondisturbance conditions

2019

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“…where C ij ≡ Q(t i )Q(t j ) is the expectation value of the measurement outcomes at time t i and t j [45,46]. This inequality holds if the dynamics of the system is classical, in the realism sense, and the measurements are noninvasive.…”

Section: Macrorealismmentioning

confidence: 99%

Hierarchy in temporal quantum correlations

Chen

Lambert

et al. 2018

Phys. Rev. A

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Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum correlation that lies in between entanglement and Bell non-locality. Its temporal analog, temporal steering, has recently been shown to have applications in quantum information and open quantum systems. Here, we show that there exists a hierarchy among the three temporal quantum correlations: temporal inseparability, temporal steering, and macrorealism. Given that the temporal inseparability can be used to define a measure of quantum causality, similarly the quantification of temporal steering can be viewed as a weaker measure of direct cause and can be used to distinguish between direct cause and common cause in a quantum network.

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“…1 eigenstates are separated from each other, and thus the counter-diabatic Hamiltonian is constructed by equation (13) or (14). In contrast, in the ordered phase, G < ( ) t J, eigenstates have 2-fold degeneracies except for the highest energy eigenstate, and thus the counter-diabatic Hamiltonian is constructed by equation (20) or (21). Originally, doubly degenerate ground states are the counterparts of the singlet and the triplet states.…”

Section: Degenerate Eigenstatesmentioning

confidence: 99%

Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions

Hatomura¹

2018

New J. Phys.

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We propose a quantum speedup method for adiabatic generation of cat states in bosonic Josephson junctions via shortcuts to adiabaticity. We apply approximated counter-diabatic driving to a bosonic Josephson junction using the Holstein-Primakoff transformation. In order to avoid the problem of divergence in counter-diabatic driving, we take finite-size corrections into account. The resulting counter-diabatic driving is well-defined over whole processes. Schedules of the counter-diabatic driving consist of three steps; the counter-diabatic driving in the disordered phase, smoothly and slowly approaching the critical point, and the counter-diabatic driving in the ordered phase. Using the counter-diabatic driving, adiabatic generation of cat states is successfully accelerated. The enough large quantum Fisher information ensures that generated cat states are highly entangled. difficulty to find shortcuts depends on the sign of the nonlinear interaction. The ground state of the antiferromagnetic Lipkin-Meshkov-Glick model is the spin-squeezed Dicke state, which is unique and has been successfully produced using shortcuts to adiabaticity with high fidelity and within short time [77,79,81]. In contrast, the ground state of the ferromagnetic Lipkin-Meshkov-Glick model is the cat state. Shortcuts to adiabaticity in the ferromagnetic Lipkin-Meshkov-Glick model was first studied by Takahashi using the Holstein-Primakoff transformation in the thermodynamic limit [78]. Counter-diabatic driving was derived for both the disordered and the ordered phases. However, this counter-diabatic driving is ill-defined, i.e., diverges, at the critical point unless the fixed-point condition is satisfied. As discussed in literatures, especially in [80], this divergence is associated with the closing of the gap and the divergence of the correlation length. Campbell et al studied counter-diabatic driving around the critical point applying various approaches, especially in combination with optimal control [80]. By applying a small longitudinal field, which enables us to slightly avoid the critical point, mean-field prescription was applied both in the invariant-based inverse engineering approach [82] and the counter-diabatic driving approach [83].In this paper, we propose approximated counter-diabatic driving for bosonic Josephson junctions without energy imbalance, which is available across the critical point, using finite-size corrections in the Holstein-Primakoff transformation. Advantages of our method are that the counter-diabatic driving is well-defined over whole processes and that schedules of the counter-diabatic driving can be analytically obtained. Using our counter-diabatic driving, we can accelerate adiabatic generation of the cat state. Schedules of the counterdiabatic driving consist of three steps. The first one is the counter-diabatic driving in the disordered phase, where we aim to let the system be in the ground state. The second one is smoothly and slowly approaching the critical point, where we give up to be adiabatic but ai...

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Leggett-Garg inequality violations with a large ensemble of qubits

Cited by 46 publications

References 57 publications

Leggett-Garg macrorealism and the quantum nondisturbance conditions

Leggett-Garg macrorealism and the quantum nondisturbance conditions

Hierarchy in temporal quantum correlations

Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions

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