© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2311.03849 · Physical Review A

Initial correlations in open quantum systems are always detectable

Iman Sargolzahi

Published Feb 12, 2024• 1 citation

Abstract

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 $t$, 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.

DOI: 10.1103/physreva.109.022213

Related papers

Witness for initial correlations among environments

F. T. Tabesh, S. Salimi, A. S. Khorashad

A quantum system inevitably interacts with its surroundings. In general, one does not have detailed information on an environment. Identifying the environmental features can help us to control the environment and its effects on the dynamics of an open system. Here, we consider a tripartite system and introduce a witness for the initial correlations among environments by means of the concept of the trace distance. Due to the existence of the initial environmental correlations, a tight upper bound is obtained for the growth of the trace distance of open quantum system states. Therefore, the initial correlations among the environments subject to particular conditions can be detected by measurements on the open system.

arXiv:1611.01975•Physical Review A•May 11, 2017•4 citations

Detecting initial system-environment correlations in open systems

Sarah Hagen, Mark Byrd

Correlations between a system and its environment lead to errors in an open quantum system. Detecting those correlations would be valuable for avoiding and/or correcting those errors. Here we show that we can detect correlations by measuring only the system itself if we know the cause of the interaction between the two, for example, in the case of a dipole-dipole interaction. We investigate the unitary $U$ which is associated with the exchange Hamiltonian and examine the ability to detect initial correlations between a system and its environment for various types of initial states. The states we select are motivated by realistic experimental conditions, and we provide bounds for when we can state with certainty that there are initial system-environment correlations given experimental data.

arXiv:2104.01695•Physical Review A•Oct 5, 2021•3 citations

Detecting initial system-environment correlations: Performance of various distance measures for quantum states

Steffen Wißmann, Bruno Leggio, Heinz‐Peter Breuer

We study the time evolution of four distance measures in the presence of initial system-environment correlations. It is well known that the trace distance between two quantum states of an open system may increase due to initial correlations, which leads to a breakdown of the contractivity of the reduced dynamics. Here we compare and analyze, for two different models, the time evolution of the trace distance, the Bures metric, the Hellinger distance, and the Jensen-Shannon divergence regarding an increase above their initial values, witnessing initial correlations. This work generalizes, deepens, and corrects a part of the study performed by Dajka et al. [Phys. Rev. A 84, 032120 (2011)] and thereby reveals generic features of the considered distance measures with respect to the capability of detecting initial system-environment correlations.

arXiv:1306.3248•Physical Review A•Aug 12, 2013•20 citations

Restrictions on initial system-environment correlations based on the dynamics of an open quantum system

Eric Chitambar, Ali Abu-Nada, Russell R. Ceballos +1 more

The dynamics of an open quantum system is often modeled by introducing a bath initially in a product state with the system, letting the system and bath evolve unitarily together, and then tracing over the bath. However, often this model may not accurately reflect a particular experimental situation. Here, we provide some restrictions on one's ability to model an open quantum system using an initial product state when some information about the system-bath interaction is known. For instance, when certain symmetries exist in the system-bath interaction, we compute limitations on how much the system's purity can be increased if the bath is initially uncorrelated white noise. Furthermore, when the system and bath are qubits, we find that effectively only swap and product unitaries always generate system dynamics capable of being modeled using an initial product state. Finally, we show how any initial correlations between the system and environment are detectable, in principle, by observing the system transformation alone during certain joint evolutions. Our results have application in experimental quantum control and quantum computing where the system and environment are often assumed to be initially uncorrelated.

Physical Review A•Nov 16, 2015•13 citations

Experimental Detection of Initial System–Environment Entanglement in Open Systems

Gaoyan Zhu, Dengke Qu, Lei Xiao +1 more

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.

Photonics•Nov 21, 2022•2 citations

Detecting Nonclassical System-Environment Correlations by Local Operations

Manuel Gessner, Heinz‐Peter Breuer

We develop a general strategy for the detection of nonclassical system-environment correlations in the initial states of an open quantum system. The method employs a dephasing map which operates locally on the open system and leads to an experimentally accessible witness for genuine quantum correlations, measuring the Hilbert-Schmidt distance between pairs of open system states. We further derive the expectation value of the witness for various random matrix ensembles modeling generic features of complex quantum systems. This expectation value is shown to be proportional to a measure for the quantum discord which reduces to the concurrence for pure initial states.

arXiv:1108.2699•Physical Review Letters•Oct 27, 2011•77 citations

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

t

, 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.

A quantum system inevitably interacts with its surroundings. In general, one does not have detailed information on an environment. Identifying the environmental features can help us to control the environment and its effects on the dynamics of an open system. Here, we consider a tripartite system and introduce a witness for the initial correlations among environments by means of the concept of the trace distance. Due to the existence of the initial environmental correlations, a tight upper bound is obtained for the growth of the trace distance of open quantum system states. Therefore, the initial correlations among the environments subject to particular conditions can be detected by measurements on the open system.

Correlations between a system and its environment lead to errors in an open quantum system. Detecting those correlations would be valuable for avoiding and/or correcting those errors. Here we show that we can detect correlations by measuring only the system itself if we know the cause of the interaction between the two, for example, in the case of a dipole-dipole interaction. We investigate the unitary

U

which is associated with the exchange Hamiltonian and examine the ability to detect initial correlations between a system and its environment for various types of initial states. The states we select are motivated by realistic experimental conditions, and we provide bounds for when we can state with certainty that there are initial system-environment correlations given experimental data.

We study the time evolution of four distance measures in the presence of initial system-environment correlations. It is well known that the trace distance between two quantum states of an open system may increase due to initial correlations, which leads to a breakdown of the contractivity of the reduced dynamics. Here we compare and analyze, for two different models, the time evolution of the trace distance, the Bures metric, the Hellinger distance, and the Jensen-Shannon divergence regarding an increase above their initial values, witnessing initial correlations. This work generalizes, deepens, and corrects a part of the study performed by Dajka et al. [Phys. Rev. A 84, 032120 (2011)] and thereby reveals generic features of the considered distance measures with respect to the capability of detecting initial system-environment correlations.

The dynamics of an open quantum system is often modeled by introducing a bath initially in a product state with the system, letting the system and bath evolve unitarily together, and then tracing over the bath. However, often this model may not accurately reflect a particular experimental situation. Here, we provide some restrictions on one's ability to model an open quantum system using an initial product state when some information about the system-bath interaction is known. For instance, when certain symmetries exist in the system-bath interaction, we compute limitations on how much the system's purity can be increased if the bath is initially uncorrelated white noise. Furthermore, when the system and bath are qubits, we find that effectively only swap and product unitaries always generate system dynamics capable of being modeled using an initial product state. Finally, we show how any initial correlations between the system and environment are detectable, in principle, by observing the system transformation alone during certain joint evolutions. Our results have application in experimental quantum control and quantum computing where the system and environment are often assumed to be initially uncorrelated.

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.

We develop a general strategy for the detection of nonclassical system-environment correlations in the initial states of an open quantum system. The method employs a dephasing map which operates locally on the open system and leads to an experimentally accessible witness for genuine quantum correlations, measuring the Hilbert-Schmidt distance between pairs of open system states. We further derive the expectation value of the witness for various random matrix ensembles modeling generic features of complex quantum systems. This expectation value is shown to be proportional to a measure for the quantum discord which reduces to the concurrence for pure initial states.