The geometry of passivity for quantum systems and a novel elementary derivation of the Gibbs state

Koukoulekidis, Nikolaos; Alexander, Rhea; Hebdige, Thomas; Jennings, David

doi:10.22331/q-2021-03-15-411

Cited by 10 publications

(8 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We prove it in basically the same way as the one used for the proof of passivity on d-dimensional quantum systems [2,3,72]. See also Theorem 4.3.53 of Ref.…”

mentioning

confidence: 83%

Quantum Ergotropy and Quantum Feedback Control

Koshihara¹,

Yuasa²

2023

Preprint

View full text Add to dashboard Cite

We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy/charging bound for unitary quantum operations. This implies that, in order to break the ergotropy/charging bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy/charging bound for unital quantum operations, applied to initial thermal equilibrium states, is tighter than the inequality representing the standard second law of thermodynamics.

show abstract

“…We prove it in basically the same way as the one used for the proof of passivity on d-dimensional quantum systems [2,3,72]. See also Theorem 4.3.53 of Ref.…”

mentioning

confidence: 83%

Quantum Ergotropy and Quantum Feedback Control

Koshihara¹,

Yuasa²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…States satisfying the above equation cannot have their energy reduced by deterministic unitary transformations. The necessary and sufficient conditions for a state to be passive require that the former commute with the Hamiltonian, i.e., , and for the eigenvalue decomposition , we find that implies for all n and m in 46 . Moreover, a state is k -passive if , with , is passive.…”

Section: Classicality and Passivitymentioning

confidence: 94%

Unravelling the non-classicality role in Gaussian heat engines

Oliveira

2022

Sci Rep

View full text Add to dashboard Cite

At the heart of quantum thermodynamics lies a fundamental question about what is genuine “quantum” in quantum heat engines and how to seek this quantumness, so that thermodynamical tasks could be performed more efficiently compared with classical protocols. Here, using the concept of P-representability, we define a function called classicality, which quantifies the degree of non-classicality of bosonic modes. This function allows us to explore the role of non-classicality in quantum heat engines and design optimal protocols for work extraction. For two specific cycles, a quantum Otto and a generalised one, we show that non-classicality is a fundamental resource for performing thermodynamic tasks more efficiently.

show abstract

“…An external system interacting with these baths reacts as if put in contact with a real qubit at the given virtual temperature [25]. Following [41,50,51], one can define virtual temperatures for a single quantum systems by constructing a set {T ij | 1 ≤ i, j ≤ d A and i|H A |i = j|H A |j }. Our result then states that the minimal and maximal virtual temperatures of a single quantum system A are operationally meaningful: They can be interpreted, respectively, as the lowest and highest temperature of a fictitious equilibrium state that can be cooled down or heated up when put in contact with A.…”

Section: Operational Definition Of Temperaturementioning

confidence: 99%

Operational definition of the temperature of a quantum state

Lipka-Bartosik¹,

Perarnau-Llobet²,

Brunner³

2022

Preprint

View full text Add to dashboard Cite

Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs) state. In this work, we propose such a notion of temperature considering an operational task, inspired by the Zeroth Law of thermodynamics. Specifically, we define two effective temperatures for quantifying the ability of a quantum system to cool down or heat up a thermal environment. In this way we can associate an operationally meaningful notion of temperature to any quantum density matrix. We provide general expressions for these effective temperatures, for both single-and many-copy systems, establishing connections to concepts previously discussed in the literature. Finally, we consider a more sophisticated scenario where the heat exchange between the system and the thermal environment is assisted by a quantum reference frame. This leads to an effect of "coherent quantum catalysis", where the use of a coherent catalyst allows for exploiting quantum energetic coherences in the system, now leading to much colder or hotter effective temperatures.

show abstract

The geometry of passivity for quantum systems and a novel elementary derivation of the Gibbs state

Cited by 10 publications

References 41 publications

Quantum Ergotropy and Quantum Feedback Control

Quantum Ergotropy and Quantum Feedback Control

Unravelling the non-classicality role in Gaussian heat engines

Operational definition of the temperature of a quantum state

Contact Info

Product

Resources

About