The interplay between two basic quantities--quantum communication and information--is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the nonlocal properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phaselike transitions when correlations become classical.
The interplay between two basic quantities--quantum communication and information--is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the nonlocal properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phaselike transitions when correlations become classical.
In spite of many results in quantum information theory, the complex nature of compound systems is far from clear. In general the information is a mixture of local and nonlocal (``quantum'') information. It is important from both pragmatic and theoretical points of view to know the relationships between the two components. To make this point more clear, we develop and investigate the quantum-information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudoclassically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal---i.e., has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other nonlocal phenomena which can be found using the paradigm of local information. For example, we prove the existence of a form of nonlocality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal. We also show that there do not exist states for which the deficit is strictly equal to the whole informational content (bound local information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proved that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.
Magic, or nonstabilizerness, is the resource that lifts Clifford circuits to universal quantum computation and has become a standard diagnostic of many-body states. For a state shared between two parties, however, a basic question has remained open: how much of the magic resides in the correlations between the parties rather than in their local bases? Isolating this nonlocal magic requires minimizing over all local bases, an optimization that has so far resisted exact solution. Here we solve it for the stabilizer fidelity: the nonlocal magic of every pure multiqubit state is the distance of its entanglement spectrum from the closest spectrum of Bell pairs. The same quantity governs an apparently unrelated task: a family of states universally embezzles entanglement under local operations and classical communication if and only if its nonlocal magic diverges. The deciding property is not the amount of entanglement but the way the entanglement spectrum spreads its weight across factor-of-two windows of rank, so that critical chains and random-singlet states, with identical logarithmic entanglement scaling, carry unbounded and vanishing nonlocal magic, respectively. Nonlocal magic thereby becomes an operationally meaningful property of quantum correlations, directly accessible to tensor-network simulations and, through entanglement spectroscopy, to experiments.
We survey progress in understanding quantum information in terms of equivalences, reducibilities, and asymptotically achievable rates for transformations among nonlocal resources such as classical communication, entanglement, and particular quantum states or channels. In some areas, eg source coding, there are straightforward parallels to classical information theory; in others eg entanglement-assisted communication, new effects and tradeoffs appear that are beginning to be fairly well understood, or the remaining uncertainty has become focussed on a few simple open questions, such as conjectured additivity of the Holevo capacity. In still other areas, e.g. the role of the back communication and the classification of tripartite entanglement, much remains unknown, and it appears unlikely that an adequate description exists in terms of a finite number of resources.
Distributed quantum computation is a task in which many distant parties perform a large quantum computation in collaboration with each other, by using classical communication, quantum communication or shared entanglement as resources.In this thesis, we consider one of the simplest nontrivial task of distributed quantum computation, that is, implementation of bipartite unitary by LOCC (local operations and classical communication) assisted by shared entanglement.Here, two input states are distributed over two distant parties.Contrary to previous researches, we consider an asymptotic scenario in which the two parties perform the same bipartite unitary on infinitely many independent input pairs.We analyze the minimum amount of resources required for the task by exploiting concepts and techniques developed in the field of quantum Shannon theory, which has originally been developed to analyze quantum communication.As a tool for analyzing distributed quantum computation, we first introduce a task that we call Markovianization.Markovianization is a task in which a tripartite pure state is transformed to a state called quantum Markov chain, by a randomizing operation on one of the three subsystems.We derive the minimum cost of randomness required for Markovianization (Markovianizing cost) by exploiting a novel decomposition of a Hilbert space introduced in the context of quantum cryptography.We then apply the obtained result to distributed quantum computation.We mainly consider implementation of bipartite unitaries by entanglement-assisted LOCC protocols consisting of three steps, called one-round protocols.This is the first nontrivial case because it is not possible to implement bipartite unitaries by protocols consisting of only one or two steps.Our main result is that we derive the minimum costs of entanglement and classical communication.We show that the minimum costs are given by the Markovianizing cost of a tripartite state associated with the unitary.The result indicates that information about input states of computation is divided into three components: one of which only information of amplitude in a basis is required for computation (information of phase is not), another of which both amplitude and phase information are required, and the other of which no information is involved in computation.Our construction of a protocol that requires the smallest amount of resources is based on this decomposition.We also propose a method to compute the Markovianizing cost of a state associated with the unitary.We also consider two-round protocols, that is, protocols consisting of concatenation of two one-round protocols, for two-qubit controlled unitaries.We show that, for a particular class of two-qubit controlled unitaries, the minimum entanglement cost in two-round protocols is strictly smaller than that in one-round protocols.This result is the first reported case that indicates a property of a trade-off relation between entanglement requirement and the number of turns in entanglement-assisted LOCC tasks.The research in this thesis opens a possibility to build a new bridge between quantum computation theory and quantum communication theory, which are the two largest subfield of quantum information theory, by analyzing a problem in the former using concepts and techniques developed in the latter.
We survey progress in understanding quantum information in terms of equivalences, reducibilities, and asymptotically achievable rates for transformations among nonlocal resources such as classical communication, entanglement, and particular quantum states or channels. In some areas, eg source coding, there are straightforward parallels to classical information theory; in others eg entanglement-assisted communication, new effects and tradeoffs appear that are beginning to be fairly well understood, or the remaining uncertainty has become focussed on a few simple open questions, such as conjectured additivity of the Holevo capacity. In still other areas, e.g. the role of the back communication and the classification of tripartite entanglement, much remains unknown, and it appears unlikely that an adequate description exists in terms of a finite number of resources.
Quantum physics provides results at information processing tasks that are unattainable by any classical theory. The aim of this thesis is to identify and characterize quantum entanglement and quantum nonlocality, the key resources used at quantum information protocols. We consider the problem of finding better experimental schemes to detect entangled states. For that, we study approximate physical realizations to non-physical processes, which provide the most efficient method to identify entanglement. We prove that many of these physical approximations have a simple experimental implementation. We then study characterization of quantum nonlocality. We introduce a method using the multipartite scenario, where more than two parties are involved, which provides several results on bipartite and multipartite quantum nonlocality. First, we prove that there exist quantum states which contain full multipartite nonlocality, which consist of the strongest kind of nonlocality. then, we prove that the combined use of several copies of a state can activate its nonlocal properties. In particular, this holds for bipartite and genuine multipartite nonlocality. Finally, we characterize quantum nonlocality by distinguishing it from stronger-than-quantum nonlocality. We construct a multipartite game for which classical and quantum players perform equally well, but for which supre-quantum players can sometimes provide an advantage. Our results suggest that physical resources might obbey a generalized no-signaling principle ( according to which ther's no instantaneous communication).