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arXiv:1903.01479 · npj Quantum Information

Quantum coherence and state conversion: theory and experiment

Kang-Da Wu, Thomas Theurer, Guo‐Yong Xiang, Chuan-Feng Li, Guang-Can Guo, Martin Bodo Plenio, Alexander Streltsov

Published Feb 13, 2020• 54 citations
arXivHTMLPDF

Abstract

Abstract The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of the resource. Here, we solve this question completely for qubit states by determining the optimal probabilities for mixed-state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion, where the process is enhanced by making use of correlations with a second party. Building on these results, we demonstrate experimentally that the optimal state-conversion probabilities can be achieved in a linear optics setup. This paves the way towards real world applications of coherence transformations in current quantum technologies.

DOI
10.1038/s41534-020-0250-z

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Abstract The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of the resource. Here, we solve this question completely for qubit states by determining the optimal probabilities for mixed-state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion, where the process is enhanced by making use of correlations with a second party. Building on these results, we demonstrate experimentally that the optimal state-conversion probabilities can be achieved in a linear optics setup. This paves the way towards real world applications of coherence transformations in current quantum technologies.
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of this resource. Here we solve this question completely for mixed states of qubits by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. This implies new lower bounds on the asymptotic state conversion rate between mixed single-qubit states which in some cases is proven to be tight. Furthermore, we obtain the minimal distillable coherence for given coherence cost among all single-qubit states, which sheds new light on the irreversibility of coherence theory.
Any quantum resource theory is based on free states and free operations, i.e., states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free operations are those which cannot create coherence for some particular experimental realization. Recently, some problems of this approach have been discussed, and new sets of operations have been proposed to resolve these problems. As an example for such a problem, a quantum operation can be incoherent in one particular experimental realization, but it still can create large amount of coherence in another. This problem is resolved by the framework of genuine quantum coherence. Here, we investigate this concept further and study other more general sets of operations which cannot create coherence in any experimental realization. We analyze in detail the mathematical structure of this class of maps and use this to study possible state transformations under these operations. We show that deterministic manipulation is severely limited, even in the asymptotic settings. In particular, this framework does not have a unique golden unit, i.e., there is no single state from which all other states can be created deterministically with the free operations. On the other hand, we show that these theories allow for a richer structure in what comes to stochastic manipulation of states. In particular, we determine the optimal probability of conversion among pure states with genuinely incoherent operations. Still, the aforementioned limitations suggest that any reasonably powerful resource theory of coherence must contain free operations which can potentially create coherence in some experimental realization.
Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between the classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological applications of quantum coherence, and limitations that arise if one is lacking the ability to establish superpositions. An important open problem in this context is a simple characterization for incoherent operations, constituted by all possible transformations allowed within the resource theory of coherence. In this Letter, we contribute to such a characterization by proving several upper bounds on the maximum number of incoherent Kraus operators in a general incoherent operation. For a single qubit, we show that the number of incoherent Kraus operators is not more than 5, and it remains an open question if this number can be reduced to 4. The presented results are also relevant for quantum thermodynamics, as we demonstrate by introducing the class of Gibbs-preserving strictly incoherent operations, and solving the corresponding mixed-state conversion problem for a single qubit.
Quantum coherence, which quantifies the superposition properties of a quantum state, plays an indispensable role in quantum resource theory. A recent theoretical work [Phys. Rev. Lett. \textbf{116}, 070402 (2016)] studied the manipulation of quantum coherence in bipartite or multipartite systems under the protocol Local Incoherent Operation and Classical Communication (LQICC). Here we present the first experimental realization of obtaining maximal coherence in assisted distillation protocol based on linear optical system. The results of our work show that the optimal distillable coherence rate can be reached even in one-copy scenario when the overall bipartite qubit state is pure. Moreover, the experiments for mixed states showed that distillable coherence can be increased with less demand than entanglement distillation. Our work might be helpful in the remote quantum information processing and quantum control.
Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be manipulated without exchanging energy with the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. We identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of energy-preserving filters increases the probability of success while reaching maximum fidelity at each iteration. Building on the recursive protocol, we construct efficient approximations of the optimal fidelity-probability trade-off, by taking coherent superpositions of the different branches generated by probabilistic filtering. The benefits of this construction are illustrated in applications to quantum metrology, quantum cloning, coherent state amplification, and ancilla-driven computation. Finally, we extend our results to transitions where the input state is generally mixed and we apply our findings to the task of purifying quantum coherence.
The resource theory of superposition is a generalization of coherence theory. A rigorous framework for quantifying superposition of linear independent states has been given by previous studies. In this paper, the optimal superposition enhancement of a mixed state is studied. Based on the l1l_{1}l1​ measure of superposition the optimal superposition enhancement value of a mixed state can be obtained under the stochastic diagonal superposition-free operations(or incomplete diagonal superposition-free operations). In addition, the optimal probability corresponding to the optimal superposition enhancement value of a mixed state is also discussed. The results show that although the superposition-free operations can decrease the superposition of a state, the superposition enhancement of a state is possible, a single mixed state can be probabilistically transformed into another state with higher superposition than before by superposition-free operations. These studies will give us a better understanding of the superposition manipulation and the resource theory of superposition.