Thermodynamic advancement in the causally inseparable occurrence of thermal maps

Guha, Tamal; Alimuddin, Mir; Parashar, Preeti

doi:10.1103/physreva.102.032215

Cited by 38 publications

(40 citation statements)

References 18 publications

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“…One of the motivations for the investigation of quantum causal structures is the prospect that indefinite causal orders could enable new quantum information processing tasks and protocols, and that causal nonseparability could be used as an information processing resource [7]. Indeed, some advantages in this respect have recently been identified, for instance in regard to quantum query complexity [12][13][14][15]30], quantum communication complexity [16,17] and other information processing tasks [18][19][20][21][22][23][24][25][26][27][28][29][31][32][33][34]. These studies have focused particularly on the quantum switch and its straightforward Noperation generalisation, since these were so far the only known examples of causally nonseparable processes with a physical interpretation.…”

Section: Applicationsmentioning

confidence: 99%

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Quantum circuits with classical versus quantum control of causal order

Wechs,

Dourdent,

Abbott

et al. 2021

Preprint

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Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum circuits, also called quantum combs. A systematic understanding of the physical interpretation of more general types of quantum supermaps-in particular, those incompatible with a definite causal structure-is however lacking. In this paper, we identify two new types of circuits that naturally generalise the fixed-order case and that likewise correspond to distinct classes of quantum supermaps, which we fully characterise. We first introduce "quantum circuits with classical control of causal order ", in which the order of operations is still well-defined, but not necessarily fixed in advance: it can in particular be established dynamically, in a classically-controlled manner, as the circuit is being used. We then consider "quantum circuits with quantum control of causal order ", in which the order of operations is controlled coherently. The supermaps described by these classes of circuits are physically realisable, and the latter encompasses all known examples of physically realisable processes with indefinite causal order, including the celebrated "quantum switch". Interestingly, it also contains new examples arising from the combination of dynamical and coherent control of causal order, and we detail explicitly one such process. Nevertheless, we show that quantum circuits with quantum control of causal order can only generate "causal" correlations, compatible with a well-defined causal order. We furthermore extend our considerations to probabilistic circuits that produce also classical outcomes, and we demonstrate by an example how the characterisations derived in this work allow us to identify new advantages for quantum information processing tasks that could be demonstrated in practice.

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Section: Applicationsmentioning

confidence: 99%

“…For QC-FOs, Proposition 2 becomes: 32 To prove Eq. (A5), one may first show (also recursively) that for any k ∈ K and any n = 0, .…”

Section: Characterisation Of Quantum Circuits With Trivialmentioning

confidence: 99%

Quantum circuits with classical versus quantum control of causal order

Wechs,

Dourdent,

Abbott

et al. 2021

Preprint

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show abstract

“…To investigate quantum coherence of temperatures arising from the above approach we now consider specifically thermalisation channels in Eqs ( 6), (7). Notably, due to the dependence of the full process on the Kraus decomposition of the individual channels, one cannot simply pick a particular Kraus decomposition without losing generality.…”

Section: B Quantum-controlled Thermalisationmentioning

confidence: 99%

“…Thus far the main focus has been on the implications of using quantum systems for temperature sensing (as thermometers) where both limitations and advantages were identified [2]; on the complementarity relation between temperature and energy fluctuations [3], which was proven to hold universally even for strongly interacting quantum systems; and an argument was even laid down for temperature to be described by an operator in quantum theory [4]. Recent work has also combined indefinite causal order and quantum thermodynamics, exploring coherent quantum control over the order of application of quantum channels [5][6][7][8][9], with claims they offer advantages in engine/cycle performances, ergotropy, etc.…”

Section: Introductionmentioning

confidence: 99%

Operational models of temperature superpositions

Wood¹,

Verma²,

Costa³

et al. 2021

Preprint

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When thermodynamical quantities are associated with quantum systems a question arises how to treat scenarios where the notion of temperature could exhibit some quantum features. It is known that the temperature of a gas in thermal equilibrium is not constant in a gravitational field, but it is not known how a delocalised quantum system would thermalise with such a bath. In this theoretical work we demonstrate two scenarios in which the notion of a 'superposition of temperatures' arises. First: a probe interacting with different baths dependent on the state of another quantum system (control). Second: the probe interacting with a bath in a superposition of purified states, each associated with a different temperature. We show that these two scenarios are fundamentally different and can be operationally distinguished. Moreover, we show that the probe does not in general thermalise even when the involved temperatures of the baths or purifications are equal. Furthermore, we show the final probe state depends on the specific realisation of the thermalising channels, being sensitive to the particular Kraus representations of the channels. This point appears to explain recent results obtained in the context of quantum interference of relativistic particle detectors thermalising with Unruh or Hawking radiation. Finally, we show that these results are reproduced in partial and pre-thermalisation processes, and thus our approach and conclusions also generally apply beyond the idealised scenarios, where thermalisation is not exact.

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“…Superpositions of causal order have become extremely relevant over the last decade. This phenomenon, known as indefinite causal order (ICO), has already been shown to break quantum limits in computation [15][16][17][18], communication [19][20][21][22][23][24][25], metrology [26][27][28][29], and thermodynamics [30][31][32], each of which were already known to outperform classical versions of the same protocols. ICO has been demonstrated in a number of groundbreaking experiments [33][34][35][36][37][38][39][40][41], many of which rely on a device known as a quantum switch to enable superpositions of the order in which unitary operations are applied to a system.…”

mentioning

confidence: 99%

Breaking the limits of purification: Postselection enhances heat-bath algorithmic cooling

Goldberg¹,

Heshami²

2021

Preprint

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Quantum technologies require pure states, which are often generated by extreme refrigeration. Heat-bath algorithmic cooling is the theoretically optimal refrigeration technique: it shuttles entropy from a multiparticle system to a thermal bath, thereby generating a quantum state with a high degree of purity. Here, we show how to surpass this hitherto-optimal technique by taking advantage of indefinite causal order. Our protocol can create arbitrary numbers of pure quantum states without any residual mixedness by using a recently-discovered device known as a quantum switch, thereby fulfilling the dream of algorithmic cooling.

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Thermodynamic advancement in the causally inseparable occurrence of thermal maps

Cited by 38 publications

References 18 publications

Quantum circuits with classical versus quantum control of causal order

Quantum circuits with classical versus quantum control of causal order

Operational models of temperature superpositions

Breaking the limits of purification: Postselection enhances heat-bath algorithmic cooling

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