Entanglement Wedge Cross Sections Require Tripartite Entanglement

We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two well-supported conjectures about the entanglement wedge cross section surface $E_W$. If $E_W$ is related to either the CFT's reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at $\mathcal{O}(\frac{1}{G_N})$. We prove that this implies holographic CFT states must have $\mathcal{O}(\frac{1}{G_N})$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.Comment: 20 pages, 5 figures, comments added in v

Quantum Reverse Shannon Theorem

Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the use of one noisy channel to simulate another. For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. In the classical case, shared randomness between sender and receiver is a sufficient auxiliary resource, regardless of the nature of the source, but in the quantum case the requisite auxiliary resources for efficient simulation depend on both the channel being simulated, and the source from which the channel inputs are coming. For tensor power sources (the quantum generalization of classical IID sources), entanglement in the form of standard ebits (maximally entangled pairs of qubits) is sufficient, but for general sources, which may be arbitrarily correlated or entangled across channel inputs, additional resources, such as entanglement-embezzling states or backward communication, are generally needed. Combining existing and new results, we establish the amounts of communication and auxiliary resources needed in both the classical and quantum cases, the tradeoffs among them, and the loss of simulation efficiency when auxiliary resources are absent or insufficient. In particular we find a new single-letter expression for the excess forward communication cost of coherent feedback simulations of quantum channels (i.e. simulations in which the sender retains what would escape into the environment in an ordinary simulation), on non-tensor-power sources in the presence of unlimited ebits but no other auxiliary resource. Our results on tensor power sources establish a strong converse to the entanglement-assisted capacity theorem.Comment: 35 pages, to appear in IEEE-IT. v2 has a fixed proof of the Clueless Eve result, a new single-letter formula for the "spread deficit", better error scaling, and an improved strong converse. v3 and v4 each make small improvements to the presentation and add references. v5 fixes broken reference

Limitations on device independent secure key via squashed non-locality

We initiate a systematic study to provide upper bounds on device-independent key, secure against a non-signaling adversary (NSDI), distilled by a wide class of operations, currently used in both quantum and non-signaling device-independent protocols. These operations consist of a direct measurements on the devices followed by Local Operations and Public Communication (MDLOPC). We employ the idea of "squashing" on the secrecy monotones, which provide upper bounds on the key rate in secret key agreement (SKA) scenario, and show that squashed secrecy monotones are the upper bounds on NSDI key. As an important instance, an upper bound on NSDI key rate called "squashed non-locality", has been constructed. It exhibits several important properties, including convexity, monotonicity, additivity on tensor products, and asymptotic continuity. Using this bound, we identify numerically a domain of two binary inputs and two binary outputs non-local devices for which the squashed non-locality is zero, and therefore one can not distil key from them via MDLOPC operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with the weight of PR box less than $80\%$. This example confirms the intuition that non-locality need not imply secrecy in the non-signaling scenario. The approach is general, describing how to construct other tighter yet possibly less computable upper bounds. Our technique for obtaining upper bounds is based on the non-signaling analog of quantum purification: the complete extension, which yields equivalent security conditions as previously known in the literature.Comment: 12 pages and 2 figures + supplemental materia

Quantum information theory of entanglement

Classical correlations are described consistently within classical information theory. This thesis presents a consistent quantum information theory of purely quantum correlations, i.e. entanglement. The main problem arises when we consider mixed states, for which it is difficult to separate quantum from purely classical correlations. This problem is the main subject of the thesis and is undertaken from two different perspectives. The first approach follows Shannon’s own approach, where we define a number of intuitively clear and physically sound conditions that a “good” measure of entanglement has to satisfy, and then search for measures satisfying these conditions. Our second approach is to extend the classical idea of distinguishing two probability distributions to quantum physics. The amount of entanglement will then determine the experimental ability to distinguish a given entangled state from a classical, disentangled state. We show that these two approaches have a number of features in common, leading to the same measures of entanglement. Classical information can be spoilt due to interactions with the environment. Classical information theory has a branch dealing with methods for protecting information called classical error correction. Quantum information is even more fragile and here we develop the quantum analogue of error correction. We develop a code that protects quantum states in the presence of spontaneous emission. We then show how to protect entanglement using this method. We also present a cavity QED implementation of various schemes aiming at increasing and protecting entanglement between two cavities using the standard Jaynes-Cummings interaction model between an atom and a cavity

The classical-quantum boundary for correlations: discord and related measures

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.Comment: Close to the published versio