Nonlocality of quantum correlations (original) (raw)
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Quantifying nonclassicality: Global impact of local unitary evolutions
Physical Review A, 2013
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord (defined via the Hilbert-Schmidt norm), thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish that two-qubit Werner states are maximally quantum correlated, and are thus the ones that maximize this type of global quantum effect. Finally, we show that similar results hold when replacing the Hilbert-Schmidt norm with the trace norm.
Fully nonlocal quantum correlations
Physical Review A, 2012
Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction pL of events admitting a local description, equal to zero. Previous examples of maximal quantum nonlocality between two parties require an infinite number of measurements, and the corresponding Bell violation is not robust against noise. We show how every proof of the Kochen-Specker theorem gives rise to maximally nonlocal quantum correlations that involve a finite number of measurements and are robust against noise. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof, providing an upper bound on the local content pL 0.22.
Physical interpretation of nonlocal quantum correlation through local description of subsystems
Scientific Reports
Characterization and categorization of quantum correlations are both fundamentally and practically important in quantum information science. Although quantum correlations such as non-separability, steerability, and non-locality can be characterized by different theoretical models in different scenarios with either known (trusted) or unknown (untrusted) knowledge of the associated systems, such characterization sometimes lacks unambiguous to experimentalist. In this work, we propose the physical interpretation of nonlocal quantum correlation between two systems. In the absence of complete local description of one of the subsystems quantified by the local uncertainty relation, the correlation between subsystems becomes nonlocal. Remarkably, different nonlocal quantum correlations can be discriminated from a single uncertainty relation derived under local hidden state (LHS)–LHS model only. We experimentally characterize the two-qubit Werner state in different scenarios.
Nonclassical correlations in subsystems of globally entangled quantum states
2021
The relation between genuine multipartite entanglement in the pure state of a collection of N qubits and the nonclassical correlations in its two-qubit subsystems is studied. Quantum discord is used as the quantifier of nonclassical correlations in the subsystem while the generalised geometric measure (GGM) [Phys. Rev. A. 81, 012308 (2010)] is used to quantify global entanglement in the N -qubit state. While no definite discernible dependence between the two can be found for randomly generated global states, for those with additional structure like weighted graph states we find that local discord is indicative of global multipartite entanglement. Global states that admit efficient classical descriptions like stabilizer states furnish an exception in which despite multipartite entanglement, nonclassical correlation is absent in two qubit subsystems. We discuss these results in the context of mixed state quantum computation where nonclassical correlation is considered a candidate reso...
Local measurement uncertainties impose a limit on nonlocal quantum correlations
Physical Review A, 2019
In quantum mechanics, joint measurements of non-commuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between non-commuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of non-local correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell's inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum non-locality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum non-locality could be explained in terms of the local characteristics of quantum statistics.
A-B Mohammad, Hichem Eleuch, and C.H.R.Ooi, 2019
We analytically investigate two separated qubits inside an open cavity field. The cavity is initially prepared in a superposition coherent state. the non-locality correlations [including trace norm measurement induced non-locality, maximal Bell-correlation, and concurrence entanglement] of the two qubits are explored. It is shown that, the generated non-locality correlations crucially depend on the decay and the initial coherence intensity of the cavity field. The enhancement of the initial coherence intensity and its superposition leads to increasing the generated non-locality correlations. The phenomena of sudden birth and death entanglement are found. Two-level system (qubit) is not only the key element in various fields of the modern physics, such as quantum optics and collision physics 1,2 , but also the fundamental building block of modern applications ranging from quantum control 3 to quantum processing 4. Due to the rapid development of experiments in macroscopic solid state physics, the artificial two-level atoms qubits based on the superconducting (SC) circuits 5,6 and quantum dots (QDs) 7 have been recognized as possible candidate for quantum processing. The SC-qubits have macroscopic quantum coherence. It may be helpful for the realization of the conditional two-qubit gate and quantum hybrid system 8,9. Embedding QD-qubits in microcav-ities enhances the light extraction efficiency via the Purcell effect and permits the study of cavity QED effects in solid-state systems 10-12. Experimentally, the qubit-photon interaction was intensively investigated 8,9,13-16. The dissipation eradicates the useful quantum coherence and correlations 17,18. The existence of dissipative qubits, such as in amorphous solids, is a longstanding problem in solid-state physics 19,20. There is a growing interest in the dynamics of non-local correlations (NLCs) beyond the quantum entangle-ment (QE) 21 , which is a unique type that has a major role in quantum processing 22. However, QE does not have all of the non-classical properties of the quantum correlations 23. While NLCs between the parts of a system in a pure state is fully characterized by their entanglement, mixed states may possess NLCs even if they are not entangled. New types of NLCs were introduced beyond QE 24 as: measurement-induced disturbance 25 , quantum discord 26 , and that was determined by using p-norms such as; the Hilbert-Schmidt norm, Schatten one-norm and Bures norm. Due to analytic difficulty to the quantum discord, the geometric correlations appeared via geometric quantum discord (GQD) and the measurement-induced nonlocality (MIN) 27 were proposed by using the 2-norm 28. However, these measurements that are based on 2-norm have been proved to be incompetent measures of NLC 29. Consequently, the GQD and MIN are derived using 1-norm (trace norm) 30-32. Moreover, non-classical correlations registered by Bell inequality violation 33 (that constitutes one of the most striking phenomena ever observed in nature) is used as an indicator of non-local quantum properties. While NLCs between the parts of a system in a pure state is fully characterized by their entanglement, mixed states may possess NLCs even if they are not entangled. Unlike entanglement, quantum discord is rather robust
Distilling nonlocality in quantum correlations
Cornell University - arXiv, 2022
Nonlocality, as established by seminal Bell's theorem, is considered to be the most striking feature of correlations present in space like separated events. Its practical application in device independent protocols, such as, secure key distribution, randomness certification etc., demands identification and amplification of such correlations observed in quantum world. In this letter we study the prospect of nonlocality distillation, wherein, by applying a natural set of free operations (called wirings) on many copies of weakly nonlocal systems, one aims to generate correlations of higher nonlocal strength. In the simplest Bell scenario, we identify a protocol, namely logical OR-AND wiring, that can distil nonlocality to significantly high degree starting from arbitrarily weak quantum nonlocal correlations. As it turns out, our protocol has several interesting facets: (i) it demonstrates that set of distillable quantum correlations has non zero measure in the full eight dimensional correlation space, (ii) it can distil quantum Hardy correlations by preserving its structure, (iii) it shows that (nonlocal) quantum correlations sufficiently close to the local deterministic points can be distilled by a significant amount. Finally, we also demonstrate efficacy of the considered distillation protocol in detecting post quantum correlations.
Quantumness of correlations revealed in local measurements exceeds entanglement
2012
The quantum world differs from our familiar classical world in many interrelated ways [1]. Quantum laws forbid basic tasks such as cloning [2] yet enable certain information processing feats otherwise unfeasible with purely classical resources [3]. In particular, quantum correlations differ from classical ones. Such a difference can assume the striking traits of entanglement [4–6] and nonlocality [7], or the subtler features of quantum discord [8].
Almost all quantum states have nonclassical correlations
Physical Review A, 2010
Quantum discord quantifies non-classical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord; and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension, and have direct implications on quantum computation and on the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.
Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
International Journal of Modern Physics B 27, 1345053, 2012
Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.