© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

International Journal of Quantum Information

Self-contained n-qubit quantum refrigerator

Mehdi Ghanavati, Hossein Movahhedian

Published Apr 1, 2014• 0 citations

Abstract

Brunner et al. [Phys. Rev. E 85 (2012) 05111] have claimed that, "essentially only the smallest machines can approach Carnot efficiency". We have verified this claim by raising self-contained four-qubit quantum refrigerator, and we have shown that according to concepts of virtual qubit, it can reach the maximum efficiency in other words Carnot efficiency. But its efficiency, such as self-contained three-qubit quantum refrigerator is not universal. We also investigated a special case of self-contained four-qubit quantum refrigerator, in other words self-contained four-qubit quantum refrigerator with two hot baths in the same temperature. We demonstrated that its efficiency has the form as efficiency of a self-contained three-qubit quantum refrigerator. In other words, from the perspective of efficiency, this particular model is equivalent to self-contained three-qubit quantum refrigerator. We also demonstrated the efficiency of this particular model in the Carnot limit that is independent from details of system model, but only depends on the environmental temperatures. Also, we raised a system that consists of n-qubit which acts as a refrigerator. According to self-contained four-qubit quantum refrigerator, we also investigated a special case of self-contained n-qubit quantum refrigerator — a self-contained n-qubit quantum refrigerator with (n - 2) baths in the same temperature. We considered the three different special situations of the n-qubit refrigerator and demonstrated their efficiency in three different situations which has the form as efficiency of self-contained three-qubit quantum refrigerator. In this special situations, (n - 2) qubits are in thermal contact with isothermal heat baths.

DOI: 10.1142/s021974991450018x

Related papers

Performance bound for quantum absorption refrigerators

Luis Alfonso Correa, José P. Palao, Gerardo Adesso +1 more

An implementation of quantum absorption chillers with three qubits has been recently proposed that is ideally able to reach the Carnot performance regime. Here we study the working efficiency of such self-contained refrigerators, adopting a consistent treatment of dissipation effects. We demonstrate that the coefficient of performance at maximum cooling power is upper bounded by 3/4 of the Carnot performance. The result is independent of the details of the system and the equilibrium temperatures of the external baths. We provide design prescriptions that saturate the bound in the limit of a large difference between the operating temperatures. Our study suggests that delocalized dissipation, which must be taken into account for a proper modeling of the machine-baths interaction, is a fundamental source of irreversibility which prevents the refrigerator from approaching the Carnot performance arbitrarily closely in practice. The potential role of quantum correlations in the operation of these machines is also investigated.

arXiv:1212.4501•Physical Review E•Apr 29, 2013•183 citations

The smallest refrigerators can reach maximal efficiency

Paul Skrzypczyk, Nicolas Brunner, Noah Linden +1 more

We investigate whether size imposes a fundamental constraint on the efficiency of small thermal machines. We analyse in detail a model of a small self-contained refrigerator consisting of three qubits. We show analytically that this system can reach the Carnot efficiency, thus demonstrating that there exists no complementarity between size and efficiency.

arXiv:1009.0865•Journal of Physics A Mathematical and Theoretical•Nov 15, 2011•114 citations

Entanglement enhances cooling in microscopic quantum refrigerators

Nicolas Brunner, Marcus Huber, Noah Linden +3 more

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

arXiv:1305.6009•Physical Review E•Mar 13, 2014•219 citations

How Small Can Thermal Machines Be? The Smallest Possible Refrigerator

Noah Linden, Sandu Popescu, Paul Skrzypczyk

We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.

arXiv:0908.2076•Physical Review Letters•Sep 21, 2010•451 citations

Quantum refrigerator driven by current noise

Yi-Xin Chen, Sheng-Wen Li

We proposed a scheme for the implementation of a "self-contained" quantum refrigerator system by three rf-SQUID qubits, or rather, flux-biased phase qubits. The three qubits play the role of the target, the refrigerator and the heat engine, respectively. We provide the three qubits with different effective temperatures, by imposing external current noises of different strengths. When the effective temperatures satisfy proper conditions, the target qubit could be cooled down. We also show that the efficiency of this system approaches the Carnot upper bound.

arXiv:1104.2363•Europhysics Letters (EPL)•Feb 1, 2012•64 citations

Entanglement enhances performance in microscopic quantum fridges

Nicolas Brunner, Marcus Huber, Noah Linden +3 more

Understanding the thermodynamics of quantum systems is of fundamental importance, from both theoretical and experimental perspectives. A growing interest has been recently given to small self-contained quantum thermal machines, the functioning of which requires no external source of work or control, but only incoherent interactions with thermal baths. The simplicity of such machines makes them and ideal test-bed for exploring quantum thermodynamics. So far, however, the importance of quantum effects in these machines has remained elusive. Here we show that entanglement, the paradigmatical quantum effect, plays a fundamental role in small self-contained quantum refrigerators, as it can enhance cooling and energy transport -- except notably when the efficiency is close to the Carnot limit. Hence a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling. More generally, our work shows that entanglement opens new possibilities in thermodynamics.

•May 26, 2013•5 citations

Brunner et al. [Phys. Rev. E 85 (2012) 05111] have claimed that, "essentially only the smallest machines can approach Carnot efficiency". We have verified this claim by raising self-contained four-qubit quantum refrigerator, and we have shown that according to concepts of virtual qubit, it can reach the maximum efficiency in other words Carnot efficiency. But its efficiency, such as self-contained three-qubit quantum refrigerator is not universal. We also investigated a special case of self-contained four-qubit quantum refrigerator, in other words self-contained four-qubit quantum refrigerator with two hot baths in the same temperature. We demonstrated that its efficiency has the form as efficiency of a self-contained three-qubit quantum refrigerator. In other words, from the perspective of efficiency, this particular model is equivalent to self-contained three-qubit quantum refrigerator. We also demonstrated the efficiency of this particular model in the Carnot limit that is independent from details of system model, but only depends on the environmental temperatures. Also, we raised a system that consists of n-qubit which acts as a refrigerator. According to self-contained four-qubit quantum refrigerator, we also investigated a special case of self-contained n-qubit quantum refrigerator — a self-contained n-qubit quantum refrigerator with (n - 2) baths in the same temperature. We considered the three different special situations of the n-qubit refrigerator and demonstrated their efficiency in three different situations which has the form as efficiency of self-contained three-qubit quantum refrigerator. In this special situations, (n - 2) qubits are in thermal contact with isothermal heat baths.

An implementation of quantum absorption chillers with three qubits has been recently proposed that is ideally able to reach the Carnot performance regime. Here we study the working efficiency of such self-contained refrigerators, adopting a consistent treatment of dissipation effects. We demonstrate that the coefficient of performance at maximum cooling power is upper bounded by 3/4 of the Carnot performance. The result is independent of the details of the system and the equilibrium temperatures of the external baths. We provide design prescriptions that saturate the bound in the limit of a large difference between the operating temperatures. Our study suggests that delocalized dissipation, which must be taken into account for a proper modeling of the machine-baths interaction, is a fundamental source of irreversibility which prevents the refrigerator from approaching the Carnot performance arbitrarily closely in practice. The potential role of quantum correlations in the operation of these machines is also investigated.

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.

We proposed a scheme for the implementation of a "self-contained" quantum refrigerator system by three rf-SQUID qubits, or rather, flux-biased phase qubits. The three qubits play the role of the target, the refrigerator and the heat engine, respectively. We provide the three qubits with different effective temperatures, by imposing external current noises of different strengths. When the effective temperatures satisfy proper conditions, the target qubit could be cooled down. We also show that the efficiency of this system approaches the Carnot upper bound.

Understanding the thermodynamics of quantum systems is of fundamental importance, from both theoretical and experimental perspectives. A growing interest has been recently given to small self-contained quantum thermal machines, the functioning of which requires no external source of work or control, but only incoherent interactions with thermal baths. The simplicity of such machines makes them and ideal test-bed for exploring quantum thermodynamics. So far, however, the importance of quantum effects in these machines has remained elusive. Here we show that entanglement, the paradigmatical quantum effect, plays a fundamental role in small self-contained quantum refrigerators, as it can enhance cooling and energy transport -- except notably when the efficiency is close to the Carnot limit. Hence a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling. More generally, our work shows that entanglement opens new possibilities in thermodynamics.