Cooling techniques are essential to understand fundamental thermodynamic questions of the lowenergy states of physical systems, furthermore they are at the core of practical applications of quantum information science. In quantum computing, this controlled preparation of highly pure quantum states is required from the state initialization of most quantum algorithms to a reliable supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. Heat-bath algorithmic cooling has been shown to purify qubits by controlled redistribution of entropy and multiple contact with a bath, not only for ensemble implementations but also for technologies with strong but imperfect measurements. In this paper, we show that correlated relaxation processes between the system and environment during rethermalization when we reset hot ancilla qubits, can be exploited to enhance purification. We show that a long standing upper bound on the limits of algorithmic cooling Schulman et al (2005 Phys. Rev. Lett. 94, 120501) can be broken by exploiting these correlations. We introduce a new tool for cooling algorithms, which we call 'state-reset', obtained when the coupling to the environment is generalized from individual-qubits relaxation to correlated-qubit relaxation. Furthermore, we present explicit improved cooling algorithms which lead to an increase of purity beyond all the previous work, and relate our results to the Nuclear Overhauser Effect.

Pure quantum states play a central role in applications of quantum information, both as initial states for quantum algorithms and as resources for quantum error correction. Preparation of highly pure states that satisfy the threshold for quantum error correction remains a challenge, not only for ensemble implementations like NMR or ESR but also for other technologies. Heat-Bath Algorithmic Cooling is a method to increase the purity of a set of qubits coupled to a bath. We investigated the achievable polarization by analysing the limit when no more entropy can be extracted from the system. In particular we give an analytic form for the maximum polarization achievable for the case when the initial state of the qubits is totally mixed, and the corresponding steady state of the whole system. It is however possible to reach higher polarization while starting with certain states, thus our result provides an achievable bound. We also give the number of steps needed to get a specific required polarization.PACS numbers: 03.67.Pp INTRODUCTIONPurification of quantum states is essential for applications of quantum information science, not only for many quantum algorithms but also as a resource for quantum error correction. The need to find a scalable way to reach approximate pure states is a challenge for many quantum computation modalities, especially the ones that relies on ensembles such as NMR or ESR [1].A potential solution is algorithmic cooling (AC), a protocol which purifies qubits by removing entropy of a subset of them, at the expense of increasing the entropy of others [2, 3]. An explicit way to implement this idea in ensemble quantum computers was given by Schulman et al. [4]. They showed that it is possible to reach polarization of order unity using only a number of qubits which is polynomial in the initial polarization. This idea was improved by adding contact with a heat-bath to extract entropy from the system [5], a process known as Heat-Bath Algorithmic Cooling (HBAC). Based on this work, many cooling algorithms have been designed [6][7][8][9][10][11]. HBAC is not only of theoretical interest, experiments have already demonstrated an improvement in polarization using this protocol with a few qubits [12][13][14][15][16][17][18], where a few rounds of HBAC were reached; and some studies have even included the impact of noise [19].Through numerical simulations, Moussa [7] and Schulman et al. [8] observed that if the polarization of the bath ( b ) is much smaller than 2 −n , where n is the number of qubits used, the asymptotic polarization reached will be ∼ 2 n−2 b ; but when b is greater than 2 −n , a polarization of order one can be reached. Inspired also by the work of Patange [20], who investigated the use of algorithmic cooling on spins bigger than 1 2 (using NV center where the defect has an effective spin 1), we investigate the case of cooling a qubit using a general spin l, and extra qubits which get contact with a bath. We found the asymptotic limit by solving the evolution equation with the results su...

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We propose a method for increasing purity of interacting quantum systems that takes advantage of correlations present due to the internal interaction. In particular we show that by using the system's quantum correlations one can achieve cooling beyond established limits of previous conventional algorithmic cooling proposals which assume no interaction.Introduction.-The field of quantum information has inspired new methods for cooling physical systems at the quantum scale [1][2][3][4][5][6][7]. Vice versa, these algorithmic cooling methods have been shown to be useful for the purification of qubits. In particular, heat-bath algorithmic cooling (HBAC) methods operate by iterating suitable redistributions of entropy and contact with a bath [1,3,[8][9][10]]. An assumption underlying current HBAC methods is that the qubits are not interacting or correlated [3][4][5][11][12][13][14]. In practice, however, the qubits generally possess correlations of both classical and quantum origin, generated thermally and through interactioninduced entanglement respectively. Here, we generalize HBAC to allow the presence of correlations -and we show that these correlations provide a resource that can be used to improve the efficiency of HBAC methods beyond previously established limits.Indeed, recent work has suggested that quantum correlations are important in work extraction and entropy flows in cooling protocols [15][16][17][18][19][20]. However, current algorithms such as PPA (Partner Pairing Algorithm [4, 9]) do not make use of correlations in the system. What is more, PPA-like algorithms include steps (rethermalization with the environment for reseting qubits) that break quantum and classical correlations in the system. Here, we improve over existing methods by instead using these pre-existing correlations to remove energy and therefore heat through so-called Quantum Energy Teleportation (QET) [15,[21][22][23][24][25][26][27][28][29]. QET allows the transmission of energy between a sender, A, and a receiver, B, without energy directly propagating from A to B. Instead, QET utilizes pre-existing quantum and classical correlations in an interacting system, together with classical (or quantum [28]) communication between A and B: First, energy is spent to measure A (classically or quantumly) and the outcome is transmitted to B. Because of the correlations, this information allows B to some extent to predict an upcoming fluctuation at his location and to extract work from it, thereby overcoming the strong local passivity of Gibbs states [15].Our aim now is to show that by combining QET methods with HBAC techniques, the purity of subsystems can