Quantum generalized subsystems

Alicki, Robert; Fannes, Mark; Pogorzelska, M.

doi:10.1103/physreva.79.052111

Cited by 15 publications

(14 citation statements)

References 16 publications

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“…There is no unique method of describing the time evolution of open quantum systems and there are several schemes to treat such systems which however typically give rise to non-equivalent dynamics [22,23]. One scheme consists in the derivation of a reduced system dynamics, via tracing over the degrees of freedom of the environment.…”

Section: Introductionmentioning

confidence: 99%

Geometric phase as a determinant of a qubit– environment coupling

Dajka

Łuczka

Hänggi

2010

Quantum Inf Process

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We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy with environment) and dissipative coupling (with exchange of energy). Reduced dynamics of the qubit is studied in terms of the rigorous Davies Markovian quantum master equation, both at zero and non-zero temperature. For pure dephasing coupling, the geometric phase varies monotonically with respect to the polar angle (in the Bloch sphere representation) parameterizing an initial state of the qubit. Moreover, it is antisymmetric about some points on the geometric phase-polar angle plane. This is in distinct contrast to the case of dissipative coupling for which the variation of the geometric phase with respect to the polar angle typically is non-monotonic, displaying local extrema and is not antisymmetric. Sensitivity of the geometric phase to details of the decoherence source can make it a tool for testing the nature of the qubit-environment interaction.

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Section: Introductionmentioning

confidence: 99%

Geometric phase as a determinant of a qubit– environment coupling

Dajka

Łuczka

Hänggi

2010

Quantum Inf Process

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“…Only the application of strong magnetic fields (compared to the topological coupling) destabilizes the topological phase [6]. However, several studies [5,7,8,9,10] and a rigorous proof [8] have shown that the toric code (TC) is not stable against thermal excitations, except in four dimensions [5,9].Therefore, the study of active error correction in topological codes [5] is fully justified. Ultimately, the goal is not only to achieve good quantum memories, but also to perform quantum computations with them.…”

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confidence: 99%

Error Threshold for Color Codes and Random Three-Body Ising Models

2009

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We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation, and faulttolerant quantum computation. We map the error-correction process onto a statistical mechanical random three-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p c ¼ 0:109ð2Þ is very close to that of Kitaev's toric code, showing that enhanced computational capabilities do not necessarily imply lower resistance to noise. DOI: 10.1103/PhysRevLett.103.090501 PACS numbers: 03.67.Pp, 03.67.Lx, 75.40.Mg, 75.50.Lk Protecting quantum states from external noise and errors is central for the future of quantum information technology. Because interaction with the environment is unavoidable, active quantum error-correction techniques based on quantum codes have been devised to restore the damaged quantum states from errors caused by decoherence [1,2]. These approaches are, in general, cumbersome and require many additional quantum bits, thus making the system more error prone. An imaginative and fruitful approach to quantum protection is to exploit topological properties of a system, e.g., by using the nontrivial topology of a surface to encode quantum states at the logical level [3]. Topology is thus considered as a resource, much like entanglement is a resource for quantum information tasks. Topological quantum computation is the combination of these two resources with the aim of winning the battle against decoherence. These topological quantum errorcorrecting codes are instances of stabilizer quantum codes [4], in which errors are diagnosed by measuring certain check operators or stabilizers. In topological codes these check operators are local, which, in practice, is an important advantage. Moreover, error correction has a deep connection to random spin models in statistical mechanics and lattice gauge theories [5].One of the original motivations for introducing surface codes was to achieve error protection at the physical level through energy barriers that would remove the need for external recovery actions. Only the application of strong magnetic fields (compared to the topological coupling) destabilizes the topological phase [6]. However, several studies [5,[7][8][9][10] and a rigorous proof [8] have shown that the toric code (TC) is not stable against thermal excitations, except in four dimensions [5,9].Therefore, the study of active error correction in topological codes [5] is fully justified. Ultimately, the goal is not only to achieve good quantum memories but also to perform quantum computations with them. In this regard, the TC [3] is somehow limited since it allows only for a convenient (transversal) implementation of a limited set of quantum gates: Pauli gates of X and Z type and the CNOT gate. To overcome this limitation, topological color codes (TCCs) have been introduced [11,12]. Using TCCs, it is possible to implement the whole Clifford group of...

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“…The map Γ is completely positive and identity preserving. This description of conditional states fits in the general setting of generalized subsystems of [4].…”

Section: Introductionmentioning

confidence: 71%