Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT correspondence, including non-uniqueness bulk operator reconstruction in boundary theory. In this article, we explore properties random tensors. We find that our naturally incorporate are analogous those correspondence. When bond dimension tensors is large,...

In the context of quantum theories spacetime, one overarching question is how information in bulk spacetime encoded holographically boundary degrees freedom. It particularly interesting to understand correspondence between subregions and order address emergence locality spacetime. For AdS/CFT correspondence, it known that this redundantly on form an error-correcting code. Having access only a subregion as if part holographic code has been damaged by noise rendered inaccessible....

With the long-term goal of studying models quantum gravity in lab, we propose holographic teleportation protocols that can be readily executed table-top experiments. These exhibit similar behavior to seen recent traversable wormhole constructions [1,2]: information is scrambled into one half an entangled system will, following a weak coupling between two halves, unscramble other half. We introduce concept by size capture how physics operator-size growth naturally leads transmission. The...

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, 4 regions, we prove that strong subadditivity monogamy mutual information give complete set inequalities. This is in contrast to situation generic quantum systems, where not known or more regions. also find an infinite new family applicable 5 The all bounds phase space entropies, defining...

Unraveling Entanglement is a curious property of some quantum mechanical systems, exploited in applications such as information processing. Walter et al. (p. 1205 ) used an algebraic geometry approach to represent the entanglement multiparticle system pure state geometric space whose axes are associated with properties individual particles. In that space, classes—collections entangled states can be transformed into each other—correspond different convex polytopes, making it possible...

Since the work of Ryu and Takayanagi, deep connections between quantum entanglement spacetime geometry have been revealed. The negative eigenvalues partial transpose a bipartite density operator is useful diagnostic entanglement. In this paper, we discuss properties associated negativity its R\'enyi generalizations in holographic duality. We first review definition negativities, which contain familiar logarithmic as special case. then study these quantities random tensor network model...

In [1] we discussed how quantum gravity may be simulated using devices and gave a specific proposal -- teleportation by size the phenomenon of size-winding. Here elaborate on what it means to do 'Quantum Gravity in Lab' size-winding connects bulk gravitational physics traversable wormholes. Perfect is remarkable, fine-grained property wavefunction an operator; show from calculation that this must hold for systems with nearly-AdS_2 bulk. We then examine detail three systems: Sachdev-Ye-Kitaev...

The unavailability of adequate HVDC circuit breakers is often named as one the key inhibitors for building multi-terminal networks. Instead only discussing what needs to be done with respect improving CB technology, we discuss other options in principle exist. None optimum itself, thus discussion must mainly driven by reviewing pros and cons from a fault current clearing point view also network planning operation view. manuscript aims at triggering stimulating on clearance than CBs.

Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions multipartite a significant challenge for general systems. In this work, we initiate study rich, yet tractable class states called stabilizer tensor networks. We demonstrate that, generic networks, geometry network informs structure state. particular, show that average number Greenberger-Horne-Zeilinger (GHZ)...

This paper initiates a systematic development of theory non-commutative optimization, setting which greatly extends ordinary (Euclidean) convex optimization. It aims to unify and generalize growing body work from the past few years developed analyzed algorithms for natural geodesically optimization problems on Riemannian manifolds that arise symmetries groups. More specifically, these are minimize moment map (a noncommutative notion usual gradient), test membership in polytopes vast class...

We propose a method to reliably and efficiently extract the fidelity of many-qubit quantum circuits composed continuously parametrized two-qubit gates called matchgates. This method, which we call matchgate benchmarking, relies on advanced techniques from randomized benchmarking as well insights representation theory circuits. argue formal correctness scalability protocol, moreover deploy it estimate performance generated by XY spin interactions processor.

Black-box models are a valuable tool to simulate dynamic arc-network interactions, such as those that occur during fault current interruption in ac or HVDC circuit breakers. However, accurate determination of characteristic arc parameters from voltage and measurements is very challenging. This paper aims improve the accuracy characterization. A new arbitrary source used simplify parameter through more complex waveform, for example, series staircase-like increasing steps. With this,...

One way to diagnose chaos in bipartite unitary channels is via the tripartite information of corresponding Choi state, which for certain choices subsystems reduces negative conditional mutual (CMI). We study this quantity from a quantum information-theoretic perspective clarify its role diagnosing scrambling. When CMI zero, we find that channel has special normal form consisting local between individual inputs and outputs. However, arbitrarily low does not imply arbitrary proximity form,...

We introduce a new correlation measure for tripartite pure states that we call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$, $B$, $C$, invariant under local unitaries, and bounded from above by $\log d_A d_B$. For random tensor network states, prove $G(A:B:C)$ equal size of minimal tripartition network, i.e., logarithmic bond dimension smallest cut partitions into three components $C$. argue holographic fixed spatial geometry, similarly computed area tripartition....

For fixed compact connected Lie groups H \subseteq G, we provide a polynomial time algorithm to compute the multiplicity of given irreducible representation in restriction an G. Our is based on finite difference formula which makes multiplicities amenable Barvinok's for counting integral points polytopes. The Kronecker coefficients symmetric group, can be seen special case such multiplicities, play important role geometric complexity theory approach P vs. NP problem. Whereas their...

The Shannon entropy of a collection random variables is subject to number constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question decide which these “laws information theory” are also respected by von Neumann many-body quantum states. In this article, we consider toy version difficult problem analyzing stabilizer We find that states satisfies all balanced inequalities hold in classical case. Our argument built on fact have model, provided...

The way in which geometry encodes entanglement is a topic of much recent interest quantum many-body physics and the AdS/CFT duality. This relation particularly pronounced case topological field theories, where topology alone determines states theory. In this work, we study set that can be prepared by Euclidean path integral three-dimensional Chern-Simons Specifically, consider arbitrary three-manifolds with fixed number torus boundaries both Abelian $U(1)$ non-Abelian $SO(3)$ For theory,...