اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Second Law of Quantum Complexity and the Entanglement Wormhole
72
0
0.0
(
0
)
تأليف
Andrea Russo
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 operator 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.
قيم البحث
اقرأ أيضاً
An entanglement measure for a bipartite quantum system is a state functional that vanishes on separable states and that does not increase under separable (local) operations. It is well-known that for pure states, essentially all entanglement measures
are equal to the v. Neumann entropy of the reduced state, but for mixed states, this uniqueness is lost. In quantum field theory, bipartite systems are associated with causally disjoint regions. There are no separable (normal) states to begin with when the regions touch each other, so one must leave a finite safety-corridor. Due to this corridor, the normal states of bipartite systems are necessarily mixed, and the v. Neumann entropy is not a good entanglement measure in the above sense. In this paper, we study various entanglement measures which vanish on separable states, do not increase under separable (local) operations, and have other desirable properties. In particular, we study the relative entanglement entropy, defined as the minimum relative entropy between the given state and an arbitrary separable state. We establish rigorous upper and lower bounds in various quantum field theoretic (QFT) models, as well as also model-independent ones. The former include free fields on static spacetime manifolds in general dimensions, or integrable models with factorizing $S$-matrix in 1+1 dimensions. The latter include bounds on ground states in general conformal QFTs, charged states (including charges with braid-group statistics) or thermal states in theories satisfying a nuclearity condition. Typically, the bounds show a divergent behavior when the systems get close to each other--sometimes of the form of a generalized area law--and decay when the systems are far apart. Our main technical tools are of operator algebraic nature.
Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to sa
y that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.
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 th
e 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.
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.
In this essay, we discuss the fine-tuning problems of the Higgs mass and the cosmological constant. We argue that these are indeed legitimate problems, as opposed to some other problems that are sometimes described using similar vocabulary. We then n
otice, following Tom Banks, that the problems become less compelling once we recognize that the Universe contains quantum gravity, and thus isnt fundamentally described by bulk QFT. Embracing this solution requires a reversal of the standard arrows UV->IR and past->future. The first reversal is familiar from AdS/CFT. The second reversal refers more specifically to our Universes cosmology, and is clearly in potential conflict with the Second Law of Thermodynamics. In the final part of the essay, we attempt to defuse this conflict, suggesting that the Second Law can arise naturally from de Sitter boundary conditions at future infinity.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
