Emergence of the Pointer Basis through the Dynamics of Correlations

Cornelio, Marcio F.; Farías, Osvaldo Jiménez; Fanchini, Felipe F.; Frérot, Irénée; Aguilar, G. H.; Hor-Meyll, M.; Oliveira, M. C. de; Walborn, S. P.; Caldeira, A. O.; Ribeiro, P. H. Souto

doi:10.1103/physrevlett.109.190402

Cited by 40 publications

(48 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Despite being motivated by Everett's relative state interpretation, pointer states presume simply an interaction between the measurement apparatus and the environment and that the observable to be measured commutes with this interaction. The study of pointer states allows not only a better understanding of a broad (and still controversial) field of interpretations of quantum mechanics, but also to follow concrete implementations in quantum theory of information -a recent example of which can be found at [81]. We hope this article can help students interested in both approaches, those who seek a more pragmatic angle, and those who want to comprehend the fundamental implications of decoherence.…”

Section: Resultsmentioning

confidence: 99%

Understanding the pointer states

Brasil¹,

Castro²

2015

Eur. J. Phys.

View full text Add to dashboard Cite

In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in the Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer state, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems -one representing the main system, the other the measurement apparatus -and a thermal bath -representing the environment -we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.

show abstract

Section: Resultsmentioning

confidence: 99%

Understanding the pointer states

Brasil¹,

Castro²

2015

Eur. J. Phys.

View full text Add to dashboard Cite

show abstract

“…2(a) and 2(b) that the tangle τ ABC (solid line in blue) quickly becomes positive, meaning that the environment C induces the global state to converge in one state that satisfies the monogamous relation. This characteristic occurs because the QD tends to decay while the classical correlation tends to be stable, at least after the transition where the classical correlation becomes greater than the quantum one [22]. More importantly, we might establish a connection between the ESD phenomenon and the balance of classical and quantum correlations.…”

Section: Tangle For a 2 × 2 × N Quantum System And Entanglement Smentioning

confidence: 99%

“…What is known is that when the set of states that minimize SE is constrained by states of the form ρ ABC = k |ψ k AB ψ k AB | ⊗ |k k|, it corresponds to the ensemble minimization employed for the derivation of the EOF, and so the SE is equal to the EOF. We see that this set corresponds to the states saturating both (22) and (23) only when there is total permutation invariance of ABC.…”

Section: Mixed Tripartite States and Squashed Entanglementmentioning

confidence: 99%

See 1 more Smart Citation

Why entanglement of formation is not generally monogamous

et al. 2013

Self Cite

View full text Add to dashboard Cite

Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if one system A is maximally entangled with another system B, it cannot be entangled at all with a third system C. This concept, known as the monogamy of entanglement, is manifest when the entanglement of A with a pair BC can be divided as contributions of the entanglement between A and B and A and C, plus a term τ ABC involving genuine tripartite entanglement and so expected to be always positive. A very important measure in quantum information theory, the entanglement of formation (EOF), fails to satisfy this last requirement. Here we present the reasons for that and show a set of conditions that an arbitrary pure tripartite state must satisfy for the EOF to become a monogamous measure, i.e., for τ ABC 0. The relation derived is connected to the discrepancy between quantum and classical correlations, τ ABC being negative whenever the quantum correlation prevails over the classical one. This result is employed to elucidate features of the distribution of entanglement during a dynamical evolution. It also helps to relate all monogamous instances of the EOF to the squashed sntanglement, an entanglement measure that is always monogamous.

show abstract

“…Moreover, we have proposed a new framework to avoid such ambiguities by independent optimization of the correlation functions. These results are relevant for a consistent correlation theory and for practical applications of correlation measures, such as in quantum many-body systems [28,29], in the emergence of the pointer basis in open quantum systems [30,31], etc. As future challenges, it remains the application of the proposed framework for states more general than the Bell-diagonal qubit-qubit states, the investigation of its robustness against decoherence, and possible relevance in quantum information tasks.…”

Section: (I)mentioning

confidence: 99%

Overcoming ambiguities in classical and quantum correlation measures

Paula¹,

Saguia²,

Oliveira³

et al. 2014

EPL

View full text Add to dashboard Cite

-We identify ambiguities in the available frameworks for defining quantum, classical, and total correlations as measured by discordlike quantifiers. More specifically, we determine situations for which either classical or quantum correlations are not uniquely defined due to degeneracies arising from the optimization procedure over the state space. In order to remove such degeneracies, we introduce a general approach where correlations are independently defined, escaping therefore from a degenerate subspace.As an illustration, we analyze the trace-norm geometric quantum discord for two-qubit Bell-diagonal states.Introduction. -Quantum correlations are widely recognized as a resource for quantum information tasks [1]. In this scenario, entanglement plays a special role for applications in quantum computation and quantum communication [2]. On the other hand, it is now known that, even in the absence of entanglement, it is possible to achieve some quantum advantage, such as in protocols for work extraction via Maxwell's demons [3], metrology [4,5], entanglement distribution [6][7][8][9][10], quantum state merging [11], among others. The source for the quantum power of such tasks can be attributed to more general quantum correlations, as measured by quantum discord [12]. Such correlations can be suitably applied to make quantum systems supersede their classical counterparts.Quantum information science has then motivated the development of a general theory of quantum, classical, and total correlations in physical systems. In this context, quantum discord has been originally introduced by Ollivier and Zurek [12] as an entropic measure of quantum correlation in a bipartite system, which arises as a difference between the total correlation (as measured by the mutual information) before and after a local measurement is performed over one of the subsystems. In addi-

show abstract

Emergence of the Pointer Basis through the Dynamics of Correlations

Cited by 40 publications

References 26 publications

Understanding the pointer states

Understanding the pointer states

Why entanglement of formation is not generally monogamous

Overcoming ambiguities in classical and quantum correlation measures

Contact Info

Product

Resources

About