Optimal quantum operations at zero energy cost

Chiribella, Giulio; Yang, Yuxiang

doi:10.1103/physreva.96.022327

Cited by 22 publications

(13 citation statements)

References 107 publications

(199 reference statements)

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“…There are some very interesting related ideas in the literature: in [24], general quantum operations costing zero energy are studied. Also, the energy cost of creating entanglement in specific many-body systems was calculated in [25].…”

Section: Introductionmentioning

confidence: 99%

Energy cost of entanglement extraction in complex quantum systems

Bény¹,

Chubb²,

Farrelly³

et al. 2018

Nat Commun

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What is the energy cost of extracting entanglement from complex quantum systems? Operationally, we may wish to actually extract entanglement. Conceptually, we may wish to physically understand the entanglement distribution as a function of energy. This is important, especially for quantum field theory vacua, which are extremely entangled. Here we build a theory to understand the energy cost of entanglement extraction. First, we consider a toy model, and then we define the entanglement temperature, relating energy cost to extracted entanglement. Next, we give a physical argument quantifying the energy cost of entanglement extraction in some quantum field vacua. There the energy cost depends on the spatial dimension: in one dimension, for example, it grows exponentially with extracted entanglement. Next, we provide approaches to bound the energy cost of extracting entanglement more generally. Finally, we look at spin chain models numerically to calculate the entanglement temperature using matrix product states.

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Section: Introductionmentioning

confidence: 99%

Energy cost of entanglement extraction in complex quantum systems

Bény¹,

Chubb²,

Farrelly³

et al. 2018

Nat Commun

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“…Our results can help to investigate phenomena such as catalytic transformations [36][37][38][39][40], and act as a starting point for the investigation of mixed state transformations, transformations in the asymptotic limit [28] or approximate transformations [41]. Akin to developments in coherence theory, we can also incorporate further physical restrictions [11] such as conservation of energy [42], or restrictions for distributed scenarios such as local superposition-free operations and classical communication [43][44][45][46]. As in coherence theory [28,44], there are also connections to entanglement theory [12,13] to be further understood.…”

mentioning

confidence: 99%

Resource Theory of Superposition

et al. 2017

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The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear independent states. This theory is a generalization of resource theories of coherence. We determine the general structure of operations which do not create superposition, find a fundamental connection to unambiguous state discrimination, and propose several quantitative superposition measures. Using this theory, we show that trace decreasing operations can be completed for free which, when specialised to the theory of coherence, resolves an outstanding open question and is used to address the free probabilistic transformation between pure states. Finally, we prove that linearly independent superposition is a necessary and sufficient condition for the faithful creation of entanglement in discrete settings, establishing a strong structural connection between our theory of superposition and entanglement theory.Introduction. -During the last decades, there has been an increasing interest in quantum technologies. The main reason for this is the operational advantages of protocols or devices working in the quantum regime over those relying on classical physics. Early examples include entanglement-based quantum cryptography [1], quantum dense coding [2] and quantum teleportation [3], where entanglement is a resource which is consumed and manipulated. Therefore the detection, manipulation and quantification of entanglement was investigated, leading to the resource theory of entanglement [4]. Typical quantum resource theories (QRTs) are built by imposing an additional restriction to the laws of quantum mechanics [5][6][7]. In the case of entanglement theory, this is the restriction to local operations and classical communication (LOCC). From such a restriction, the two main ingredients of QRTs emerge: The free operations and the free states (which are LOCC and separable states in the case of entanglement theory). All states which are not free contain the resource under investigation and are considered costly. Therefore free operations must transform free states to free states, allowing for the resource to be manipulated but not freely created. Once these main ingredients are defined, a resource theory investigates the manipulation, detection, quantification and usage of the resource.In principle, not only entanglement but every property of quantum mechanics not present in classical physics could lead to an operational advantage [8,9]. This motivates the considerable interest in the rigorous quantification of nonclassicality [10][11][12][13][14][15]. The superposition principle underlies many non-classical properties of quantum mechanics including entanglement or coherence. Recently resource theories of coherence [11,16,17] and their role in fields as diverse as quantum computation [8,18,19], quantum phase discrimination [20] and quantum thermodynamics [21] attracted considerable attenti...

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“…For a continuous time evolution of a closed system, energy conservation throughout the process requires [H(t), U ] = 0 ∀t [50], where H(t) = H 0 +V (t) and V (t) is the interaction Hamiltonian. The unitary evolution from time t 1 to t 2 can be given by a unitary U (t) of the form…”

Section: Theoremmentioning

confidence: 99%

Role of Coherence and Degeneracies in Quantum Synchronisation

Solanki,

Jaseem,

Hajdušek

et al. 2021

Preprint

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Progress on the study of synchronisation in quantum systems has been largely driven by specific examples which resulted in several examples of frequency entrainment as well as mutual synchronisation. Here we study quantum synchronisation by utilising Liouville space perturbation theory. We begin by clarifying the role of centers, symmetries and oscillating coherences in the context of quantum synchronisation. We then analyse the eigenspectrum of the Liouville superoperator generating the dynamics of the quantum system and determine the conditions under which synchronisation arises. We apply our framework to derive a powerful relationship between energy conservation, degeneracies and synchronisation in quantum systems. Finally, we demonstrate our approach by analysing two mutually coupled thermal machines and the close relationship between synchronisation and thermodynamic quantities.

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Optimal quantum operations at zero energy cost

Cited by 22 publications

References 107 publications

Energy cost of entanglement extraction in complex quantum systems

Energy cost of entanglement extraction in complex quantum systems

Resource Theory of Superposition

Role of Coherence and Degeneracies in Quantum Synchronisation

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