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Photonics

Experimental Detection of Initial System–Environment Entanglement in Open Systems

Gaoyan Zhu, Dengke Qu, Lei Xiao, Peng Xue

Published Nov 21, 2022• 2 citations
Publisher

Abstract

We experimentally investigate how initial entanglement between the system and environment can be detected in an open system by using some prior knowledge of the joint evolutions. The protocol we employed requires classical optimization on the results after performing measurements on the system state. Such an approach does not require a full 2-qubit QST, and works in scenarios where one has access to the system only. We demonstrate the protocol on both pure entangled states and mixed entangled states. The obtained results show the experimental accessibility and validity of the protocol. Compared with the previous methods, which also assume access only to the system, this protocol is less demanding in terms of measurement and state preparation. The experimental results also show that, using the knowledge of the interaction, we can fine-tune the protocol, thus showing the potential of the protocol for developing experimentally feasible and practical entanglement detection methods.

DOI
10.3390/photonics9110883

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We experimentally investigate how initial entanglement between the system and environment can be detected in an open system by using some prior knowledge of the joint evolutions. The protocol we employed requires classical optimization on the results after performing measurements on the system state. Such an approach does not require a full 2-qubit QST, and works in scenarios where one has access to the system only. We demonstrate the protocol on both pure entangled states and mixed entangled states. The obtained results show the experimental accessibility and validity of the protocol. Compared with the previous methods, which also assume access only to the system, this protocol is less demanding in terms of measurement and state preparation. The experimental results also show that, using the knowledge of the interaction, we can fine-tune the protocol, thus showing the potential of the protocol for developing experimentally feasible and practical entanglement detection methods.
Decoherence is an unavoidable effect of the quantum system coupled to an environment, which leads to the system evolving from a pure state to a mixed one. A critical issue here is that the reduction of purity is quantum or classical, which corresponds to whether or not entanglement is generated between the system and environment. We report a proof-of-principle experimental investigation of such entanglement in a simple but paradigmatic case, in which a qubit system interacts with a pure dephasing channel. The pure dephasing process is realized in a linear photonic system, and the experiment is a validation in a very controlled setting. By adopting previous methods to detect qubit-environment entanglement, we prove that such entanglement can be detected by performing local measurements on only one subsystem, even when the other subsystem in the pair cannot be detected. Our experiment paves the way for investigating features of open quantum system dynamics.
Abstract We propose a scheme for the detection of qubit–environment entanglement which requires only operations and measurements on the qubit, all within reach of current experimental state-of-the-art. The scheme works for any type of interaction which leads to pure dephasing of the qubit as long as the initial qubit state is pure. The scheme is direct in the sense that it allows the detection of entanglement present in the system at time τ\tau τ τ after the initialization of the qubit in a superposition state. It requires a measurement on the qubit at time τ\tau τ τ and a comparison of the post-measurement evolution to the evolution obtained by a modified scheme. It becomes particularly simple when one of the qubit states is neutral with respect to the environment, such as in case of the most common choice of the NV center spin qubit or for excitonic charge qubits, when the environment is initially at thermal equilibrium. In this case, the post-measurement evolution needs to be compared only to the standard decoherence which is obtained without any qubit manipulation after the preparation of the initial state.
Decoherence is a manifestation of the coupling of a system with its environment. The resulting loss of information can hamper the functioning of quantum devices; hence, there is a need to understand its origin and dynamics. Decoherence can stem from entanglement, but it can also be classical in nature. Indeed, methods have been developed to understand whether qubit-environment entanglement (QEE) is actually present in some important classes of quantum channels—pure dephasing. Their practicality resides in the fact that they only require accessing the system qubit. In this paper, we show an implementation of this technique in a photonic quantum channel simulator via a scheme that has been tailored to the system under study. By controlling the input state of the environment in our simulation, we can check the occurrence of qubit environment entanglement in simple, yet insightful test cases. Our results showcase the usefulness and experimental relevance of the QEE witnessing technique.
Consider an open quantum system which interacts with its environment. Assuming that the experimenter has access only to the system, an interesting question is whether it is possible to detect initial correlations between the system and the environment by performing measurements only on the system. Various methods have been proposed to detect correlations by local measurements on the system. After reviewing these methods, we will show that initial correlations between the system and the environment are always detectable. In particular, we will show that one can always find a unitary evolution, for the whole system-environment, such that the trace distance method, proposed to witness correlations locally, succeeds. We also find the condition for existence of the optimal unitary evolution, for which the entire correlation is locally detectable. Next, we address the case where the system and the environment interact through a time-independent Hamiltonian. For this case we will see that if the initial correlation can be detected locally at some time ttt, then it can be detected for almost all the other times too. On the other hand, we see that one can find cases for which initial correlations between the system and the environment always remain undetectable even though the unitary evolution, generated by the Hamiltonian, is not factorized.
We experimentally demonstrate a method for detection of entanglement via construction of entanglement witnesses from a limited fixed set of local measurements ( M ). Such a method does not require a priori knowledge about the form of the entanglement witnesses. It is suitable for a scenario where a full state tomography is not available, but the only resource is a limited set of M . We demonstrate the method on pure two-qubit entangled states and mixed two-qubit entangled states, which emerge from photonic implementation of controllable quantum noisy channels. The states we select are motivated by realistic experimental conditions, and we confirm it works well for both cases. Furthermore, possible generalizations to higher-dimensional bipartite systems have been considered, which can potentially detect both decomposable and indecomposable entanglement witnesses. Our experimental results show perfect validity of the method, which indicates that even a limited set of local measurements can be used for quick entanglement detection and further provide a practical test bed for experiments with entanglement witnesses.