ترغب بنشر مسار تعليمي؟ اضغط هنا

Second Law of Entanglement Dynamics for the Non-Asymptotic Regime

221   0   0.0 ( 0 )
 نشر من قبل Mark Wilde
 تاريخ النشر 2021
والبحث باللغة English
 تأليف Mark M. Wilde




اسأل ChatGPT حول البحث

The distillable entanglement of a bipartite quantum state does not exceed its entanglement cost. This well known inequality can be understood as a second law of entanglement dynamics in the asymptotic regime of entanglement manipulation, excluding the possibility of perpetual entanglement extraction machines that generate boundless entanglement from a finite reserve. In this paper, I establish a refined second law of entanglement dynamics that holds for the non-asymptotic regime of entanglement manipulation.



قيم البحث

اقرأ أيضاً

71 - Andrea Russo 2021
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex unitary ope rator capable of transforming one state into the other. Starting with K qubits evolving through a k-local Hamiltonian, it is possible to draw an analogy between the quantum system and an auxiliary classical system. Using the definition of complexity to define a metric for the classical system, it is possible to relate its entropy with the quantum complexity of the K qubits, defining the Second Law of Quantum Complexity. The law states that, if it is not already saturated, the quantum complexity of a system will increase with an overwhelming probability towards its maximum value. In the context of AdS/CFT duality and the ER=EPR conjecture, the growth of the volume of the Einstein Rosen bridge interior is proportional to the quantum complexity of the instantaneous state of the conformal field theory. Therefore, the interior of the wormhole connecting two entangled CFT will grow as a natural consequence of the complexification of the boundary state.
We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassens theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichoto mies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Renyi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing.
We discuss quantum capacities for two types of entanglement networks: $mathcal{Q}$ for the quantum repeater network with free classical communication, and $mathcal{R}$ for the tensor network as the rank of the linear operation represented by the tens or network. We find that $mathcal{Q}$ always equals $mathcal{R}$ in the regularized case for the samenetwork graph. However, the relationships between the corresponding one-shot capacities $mathcal{Q}_1$ and $mathcal{R}_1$ are more complicated, and the min-cut upper bound is in general not achievable. We show that the tensor network can be viewed as a stochastic protocol with the quantum repeater network, such that $mathcal{R}_1$ is a natural upper bound of $mathcal{Q}_1$. We analyze the possible gap between $mathcal{R}_1$ and $mathcal{Q}_1$ for certain networks, and compare them with the one-shot classical capacity of the corresponding classical network.
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and in stark contra st to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Steins Lemma proved in [Brandao and Plenio, Commun. Math. 295, 791 (2010)], giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.
184 - Chien-Hao Lin , Yew Kam Ho 2014
In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns 1Se states (with n = 1 to 6) and triplet-spin 1sns 3Se states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt-Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا