<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric slowing down of decoherence

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

doi:10.1103/physreva.94.040101

Cited by 42 publications

(31 citation statements)

References 82 publications

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“…In the preceding subsections we presented the case for the Bures angle, which is the generalised geometric angle between density operators. However, for many applications one is not necessarily interested in how exactly the quantum states evolve, but one rather needs a quick estimate of, for instance, the typical flow of entropy [177] or the rate of decoherence [178]. Thus, a plethora of other speed limits have been discussed in the literature.…”

Section: Quantum Speed Limits For Other Quantitiesmentioning

confidence: 99%

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

Deffner

Campbell

2017

J. Phys. A: Math. Theor.

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One of the most widely known building blocks of modern physics is Heisenberg's indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this Topical Review we describe important milestones, such as the Mandelstam-Tamm and the Margolus-Levitin bounds on the quantum speed limit, and summarise recent applications in a variety of current research fields -including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach, where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this Topical Review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader.

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Section: Quantum Speed Limits For Other Quantitiesmentioning

confidence: 99%

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

Deffner

Campbell

2017

J. Phys. A: Math. Theor.

Self Cite

485

439

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“…Among the nontrivial phenomena observed in these experiments are unidirectional invisibility in fiber networks [8], nonreciprocal light transport in whispering gallery microresonators [7], single-mode lasing in otherwise multimoded lasers with PT -symmetry [23,24], loss-induced lasing [6], control of emission direction of lasing in microring lasers [9], a mobility edge in disordered optical waveguide arrays [25,26], as well as chiral dynamics [16] and topological energy transfer when encircling an EP [19]. Recent years have also seen a number of very interesting theoretical proposals revealing how PT -symmetry can be used to enhance and control optomechanical interactions, and how PT -symmetry affects quantum phase transitions and information retrieval in quantum systems [27][28][29]. For example, the works of Jing et al with optomechanical microresonators have revealed the possibility of thresholdless phonon lasing [30], group veloc-1L 2L 1R 2R FIG.…”

Section: Introductionmentioning

confidence: 99%

PT -symmetric circuit QED

et al. 2018

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The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but PT -symmetric Hamiltonians may also have real eigenvalues. Systems described by such effective PT -symmetric Hamiltonians have been realized in experiments using coupled systems with balanced loss (dissipation) and gain (amplification), and their corresponding classical dynamics has been studied. A PT -symmetric system emerging from a quantum dynamics is highly desirable, in order to understand what PT -symmetry and the powerful mathematical and physical concepts around it will bring to the next generation of quantum technologies. Here, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator). By means of external driving fields on the qubits, we are able to tune gain and losses in the resonators. Starting with the quantum dynamics of this system, we show the emergence of the PT -symmetry via the selection of both driving amplitudes and frequencies. We engineer the system such that a non-number conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths. The PT -symmetry and its breaking, as well as the predicted instability in this circuit-QED system can be observed in a transmission experiment. arXiv:1801.06678v1 [quant-ph]

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“…This is because that experimental quantum systems are governed by Hermitian Hamiltonians. A possible approach is to realize a PT symmetric Hamiltonian in an open quantum system, but it is generally difficult to realize a controllable PT symmetric Hamiltonian by controlling the environment [22]. Some progress has been made with this approach in the system of light-matter quasiparticles [23,24].…”

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confidence: 99%

Observation of parity-time symmetry breaking in a single-spin system

Liu

Geng

et al. 2019

Science

356

278

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A fundamental axiom of quantum mechanics requires the Hamiltonians to be Hermitian which guarantees real eigen-energies and probability conservation. However, a class of non-Hermitian Hamiltonians with Parity-Time (PT ) symmetry can still display entirely real spectra [1]. The Hermiticity requirement may be replaced by PT symmetry to develop an alternative formulation of quantum mechanics [2, 3]. A series of experiments have been carried out with classical systems including optics [4], electronics [5][6][7], microwaves[8], mechanics [9] and acoustics [10][11][12]. However, there are few experiments to investigate PT symmetric physics in quantum systems. Here we report the first observation of the PT symmetry breaking in a single spin system. We have developed a novel method to dilate a general PT symmetric Hamiltonian into a Hermitian one, which can be realized in a practical quantum system. Then the state evolutions under PT symmetric Hamiltonians, which range from PT symmetric unbroken to broken regions, have been experimentally observed with a single nitrogen-vacancy (NV) center in diamond. Due to the universality of the dilation method, our result opens a door for further exploiting and understanding the physical properties of PT symmetric Hamiltonian in quantum systems. arXiv:1812.05226v1 [quant-ph]

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PT-symmetric slowing down of decoherence

Cited by 42 publications

References 82 publications

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

PT -symmetric circuit QED

Observation of parity-time symmetry breaking in a single-spin system

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