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arXiv:quant-ph/0504148 · New Journal of Physics

Work extraction from tripartite entanglement

Vincent Viguié, Koji Maruyama, Vlatko Vedral

Published Sep 16, 2005• 17 citations
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Abstract

It has recently been shown that the work extractable from correlated bipartite quantum systems under an appropriate protocol can be used to distinguish entanglement from classical correlation. A natural question is now whether it can be generalized to multipartite systems. In this paper, we devise a protocol to distinguish the GHZ, the W, and separable states in terms of the thermodynamically extractable work under local operations and classical communication, and compare the results with those obtained from Mermin's inequalities.

DOI
10.1088/1367-2630/7/1/195

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It has recently been shown that the work extractable from correlated bipartite quantum systems under an appropriate protocol can be used to distinguish entanglement from classical correlation. A natural question is now whether it can be generalized to multipartite systems. In this paper, we devise a protocol to distinguish the GHZ, the W, and separable states in terms of the thermodynamically extractable work under local operations and classical communication, and compare the results with those obtained from Mermin's inequalities.
Abstract A thermodynamic theory of quantum entanglement as well as the establishment of rigorous formal connections between the laws of thermodynamics and the phenomenology of entanglement are currently open areas of investigation. In this quest, a core problem is embodied by the understanding of the role that entanglement plays in processes of work extraction. Here, by considering information thermodynamics-based protocols, we answer the question “Is it possible to infer, quantitatively, quantum correlations by considering work-extraction schemes?”. Our experimental settings consist of suitably designed multi-photon optical interferometers able to address the case of both bipartite and multipartite entangled states. We compare the performance of such criteria to that of witnesses of entanglement based on the violation of Bell-like tests, showing their inherently different nature. Our work contributes strongly to the ongoing efforts in establishing photonic systems as a platform for experiments in information thermodynamics.
Multipartite entanglement purification is revisited by using the Local operations and classical communications(LOCCs). We demonstrate our idea by considering the tripartite case, i.e. the purification of tripartite entanglement. We express the general tripartite entangled states in a special representation of total spin operators J1232J_{123}^{2}J1232​ and % J_{12}^{2} of tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a \textit{genuine basis} because it consists of of all the genuine entangled states of tripartite system. Our protocol is a recurrence one, and only two copies of the initial mixed tripartite entangled states are needed in each round. It is shown that if the initial fidelity is larger than a threshold 0.4, the purification process will succeed.The yield of the current protocol is higher than the previous multipartite entanglement purification protocols. As a by-product, we can get a bipartite pure Bell state when the purification protocol fails for W state. Our protocol also shows that there may be some special kind of tripartite entanglement which belongs to neither W-type entanglement nor GHZ-type entanglement.
The phenomenon of quantum entanglement is a fundamental feature of quantum mechanics which, as a counterintuitive and inherently ”quantum” phenomenon (with no classical analogue) has been the subject of much study, especially in quantum information theory. One fruitful approach to the description of entanglement has been in its operational description - that is, in the consideration of what can be achieved using entangled states under certain restrictions, typically the regime of local operations and classical communications.\n\nWe present results here related to the operational characterisation of entanglement in the resource model, in both bipartite and multipartite cases. First, we consider the conversion between pure bipartite entangled states in terms of an often-ignored resource - the classical communication cost. Using prior results for more specific conversions, we derive lower bounds on this cost (and the related quantity of the conversion inefficiency) for general bipartite pure states.\n\nWe also consider pure-state conversions of multipartite entanglement, in particular the class of protocols in which multipartite states are converted to states shared between fewer parties. We have found a previously-unconsidered variety of such conversions, in which the target state of the conversion is a state shared between a random subset of the parties. We find that when such post-selection of parties in the protocol is permitted allows for a wider variety of achievable target states; certain states which can not be reliably obtained between predetermined parties (even some where the probability of doing so is arbitrarily small) can be obtained between random parties. We consider a variety of states in which this phenomenon occurs, as well as bounds on such protocols can achieve.\n\nFinally we consider a practical use of entanglement as a resource, in an experimental implementation of a multipartite QKD protocol. This is based on the tripartite GHZ entangled state, but can be implemented using only bipartite entanglement. We adapt existing QKD results for both the bipartite and multipartite case to derive a secure key rate for this implementation, taking into account the ways in which it differs from the idealised theoretical case.
Understanding the thermal behavior of quantum many-body pure states is one of the most fundamental issues in quantum thermodynamics. It is widely known that typical pure states yield vanishing work, just as thermal states do, when one restricts to local operations that cannot access correlations among subsystems. However, it remains unclear whether this equivalence to thermal states persists under LOCC (local operations and classical communication), where classically accessible correlations can be exploited for work extraction. In this work, we establish criteria for determining whether many-body pure states remain equivalent to thermal states even under LOCC, and show that this thermal equivalence is governed by their multipartite quantum correlation structure. We show that states with asymptotically maximal multipartite entanglement, such as Haar-random states, cannot yield extensive work under LOCC, whereas some states with limited multipartite entanglement, such as constant-degree graph states, allow extensive work extraction despite being locally indistinguishable from thermal states. Thus, our work provides a refined operational notion of thermal equivalence beyond the traditional local regime, which is becoming increasingly important due to the recent expansion of experimentally accessible operations.
While bipartite quantum correlations have been extensively studied across various fields, the role of multipartite quantum correlations in many-body systems remains elusive due to their complex structure. A primary challenge lies in the fact that the calculation of multipartite quantum correlation measure often requires an exponential cost with respect to the system size. In this work, we address this problem by adopting a thermodynamic approach: We introduce a measure of multipartite quantum correlations based on the difference in extractable thermodynamic work between global operations and LOCC (local operations and classical communication). This can be regarded as a multipartite generalization of the bipartite work deficit, which has attracted attention as a thermodynamic measure of bipartite quantum correlation. Importantly, we develop an efficient method for computing the multipartite work deficit in a special class of quantum many-body systems described by matrix product states (MPS). The numerical cost of this method scales linearly with system size, significantly reducing the exponential overhead required for direct calculations. We apply this method to an MPS family and show that a quantum phase transition is well captured by the multipartite work deficit, which exhibits singular behavior at the transition point. Our work shows that the multipartite work deficit not only highlights the fundamental connection between multipartite quantum correlations and quantum thermodynamics, but also serves as an efficiently computable probe of the structures of quantum many-body systems.