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arXiv:2209.03976 · Journal of Physics A Mathematical and Theoretical

The transfer of entanglement negativity at the onset of interactions

Robin Y. Wen, Achim Kempf

Published Nov 30, 2022• 5 citations
arXivHTMLPDF

Abstract

Abstract Quantum information, in the form of entanglement with an ancilla, can be transmitted to a third system through interaction. Here, we investigate this process of entanglement transmission perturbatively in time. Using the entanglement monotone negativity, we determine how the proclivity of an interaction to either generate, transfer or lose entanglement depends on the choice of Hamiltonians and initial states. These three proclivities are captured by Hamiltonian- and state-dependent quantities that we call negativity susceptibility, negativity transmissibility and negativity vulnerability respectively. These notions could serve, for example, as cost functions in quantum technologies such as machine-learned quantum error correction.

DOI
10.1088/1751-8121/aca7a1

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Abstract Quantum information, in the form of entanglement with an ancilla, can be transmitted to a third system through interaction. Here, we investigate this process of entanglement transmission perturbatively in time. Using the entanglement monotone negativity, we determine how the proclivity of an interaction to either generate, transfer or lose entanglement depends on the choice of Hamiltonians and initial states. These three proclivities are captured by Hamiltonian- and state-dependent quantities that we call negativity susceptibility, negativity transmissibility and negativity vulnerability respectively. These notions could serve, for example, as cost functions in quantum technologies such as machine-learned quantum error correction.
We show that, for the purpose of quantum communication via a quantum field, it is essential to view the field not only as a medium for transmission but also as a source of entanglement that can aid in the communication task. To this end, we consider the quantum communication scenario where Alice is initially entangled with an ancilla and intends to communicate with Bob through a quantum field, so as to make Bob entangled with the ancilla. We find that if Alice and Bob communicate by directly coupling to the quantum field, then they can generate negativity between Bob and the ancilla only at orders that are higher than second perturbative order. We then present a protocol based on quantum teleportation in which Alice and Bob consume entanglement that they obtained from the field via interaction or harvesting. We show that this protocol can transfer negativity already to second perturbative order.
This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems R and Q, after which Q is subjected to a dynamical evolution given by the superoperator EQ{\mathit{E}}^{\mathit{Q}}EQ. Two interesting quantities can be defined for this process: the entanglement fidelity Fe{\mathit{F}}_{\mathit{e}}Fe​ and the entropy exchange Se{\mathit{S}}_{\mathit{e}}Se​. It turns out that neither of these quantities depends in any way on the system R, but only on the initial state and dynamical evolution of Q. Fe{\mathit{F}}_{\mathit{e}}Fe​ and Se{\mathit{S}}_{\mathit{e}}Se​ are related to various other fidelities and entropies and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes. \textcopyright{} 1996 The American Physical Society.
This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems RRR and QQQ, after which QQQ is subjected to a dynamical evolution given by the superoperator $\superop^{Q}$. Two interesting quantities can be defined for this process: the entanglement fidelity FeF_{e}Fe​ and the entropy production SeS_{e}Se​. It turns out that neither of these quantities depends in any way on the system RRR, but only on the initial state and dynamical evolution of QQQ. FeF_{e}Fe​ and SeS_{e}Se​ are related to various other fidelities and entropies, and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.
Abstract In this work, we investigate the parameters governing the rate at which a quantum channel arises at the onset of an interaction between two systems, A and B . In particular, when system A is pre-entangled with an ancilla, A ~ , we quantify the early-time transmission of pre-existing entanglement by calculating the leading order change in coherent information of the complementary channel ( A → B ′). We show that, when A and B are initially unentangled and B is pure, there is no change in coherent information to first order, while the leading (second) order change is divergent. However, this divergence may be regulated by embedding the conventional notion of coherent information into what we call the family of n -coherent informations, defined using n -Rényi entropies. We find that the rate of change of the n -coherent information at the onset of the interaction is governed by a quantity, which we call the n -exposure, which captures the extent to which the initial coherent information of A with A ~ is exposed to or ‘seen by’ the interaction Hamiltonian between A and B . We give examples in qubit systems and in the light–matter interaction.
Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose an operational scheme to measure the entanglement --- as given by the negativity --- between arbitrary subsystems of size NAN_ANA​ and NBN_BNB​, with O(NA+NB)\mathcal{O}(N_A + N_B)O(NA​+NB​) measurements, and without any prior knowledge of the state. We propose how to experimentally measure the partially transposed moments of a density matrix, and using just the first few of these, extract the negativity via Chebyshev approximation or machine learning techniques. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.
Abstract At the onset of an interaction between two initially independent systems, each system tends to experience an increase in its n -Rényi entropies, such as its von Neumann entropy ( n = 1) and its mixedness ( n = 2). We here ask which properties of a system determine how quickly its Rényi entropies increase and, therefore, how sensitive the system is to becoming entangled. We find that the rate at which the n -Rényi entropy increases in an interaction is determined by a quantity which we term the n -fragility of the system. The 2-fragility is closely related to the notion of 2-norm coherence, in that it too quantifies the extent to which a density matrix is ‘off-diagonal’ with respect to the eigenbasis of a reference operator. Nevertheless, the 2-fragility is not a coherence monotone in the resource theoretic sense since it depends also on the eigenvalues of the reference operator. It is this additional sensitivity to the eigenvalues of the reference operator, here the interaction Hamiltonian, which enables the 2-fragility to quantify the rate of entropy production in interactions. We give an example using the light–matter interaction and we anticipate applications to the study of the rates at which two systems exchange classical and quantum information when starting to interact.