"Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny

The possibility of maintaining entanglement in a quantum system at finite, even high, temperatures -- the so-called `hot entanglement' -- has obvious practical interest, but also requires closer theoretical scrutiny. Since quantum entanglement in a system evolves in time and is continuously subjected to environmental degradation, a nonequilibrium description by way of open quantum systems is called for. To identify the key issues and the contributing factors that may permit `hot entanglement' to exist, or the lack thereof, we carry out a model study of two spatially-separated, coupled oscillators in a shared bath depicted by a finite-temperature scalar field. From the Langevin equations we derived for the normal modes and the entanglement measure constructed from the covariance matrix we examine the interplay between direct coupling, field-induced interaction and finite separation on the structure of late-time entanglement. We show that the coupling between oscillators plays a crucial role in sustaining entanglement at intermediate temperatures and over finite separations. In contrast, the field-induced interaction between the oscillators which is a non-Markovian effect, becomes very ineffective at high temperature. We determine the critical temperature above which entanglement disappears to be bounded in the leading order by the inverse frequency of the center-of-mass mode of the reduced oscillator system, a result not unexpected, which rules out hot entanglement in such settings.Comment: 13 pages, 2 figure

Quantum Channel Capacities with Passive Environment Assistance

We initiate the study of passive environment-assisted communication via a quantum channel, modeled as a unitary interaction between the information carrying system and an environment. In this model, the environment is controlled by a benevolent helper who can set its initial state such as to assist sender and receiver of the communication link. (The case of a malicious environment, also known as jammer, or arbitrarily varying channel, is essentially well-understood and comprehensively reviewed.) Here, after setting out precise definitions, focussing on the problem of quantum communication, we show that entanglement plays a crucial role in this problem: indeed, the assisted capacity where the helper is restricted to product states between channel uses is different from the one with unrestricted helper. Furthermore, prior shared entanglement between the helper and the receiver makes a difference, too.Comment: 14 pages, 13 figures, IEEE format, Theorem 9 (statement and proof) changed, updated References and Example 11 added. Comments are welcome

Noisy Embezzlement of Entanglement and Applications to Entanglement Dilution

In this thesis we present the concept of embezzlement of entanglement, its properties, efficiency, possible generalizations and propose the linear programming characterization of this phenomenon. Then, we focus on the noisy setting of embezzlement of entanglement. We provide the detailed proof of the quantum correlated sampling lemma which can be considered a protocol for noisy embezzlement of entanglement. Next, we propose a classical synchronization scheme for two spatially separated parties which do not communicate and use shared randomness to synchronize their descriptions of a quantum state. The result, together with the canonical embezzlement of entanglement, improves the quantum correlated sampling lemma for small quantum states in terms of the probability of success and distance between desired and final states. Then, we discuss the role of entanglement spread in dilution of entanglement. We propose an explicit protocol for the task of dilution of entanglement without communication. The protocol uses EPR pairs and an embezzling state of a relatively small size for the task of diluting entangled quantum states up to small infidelity. We modify the protocol to work in a noisy setting where the classical synchronization scheme finds its application

Absolutely Maximally Entangled States: Existence and Applications

We investigate absolutely maximally entangled (AME) states, which are multipartite quantum states that are maximally entangled with respect to any possible bipartition. These strong entanglement properties make them a powerful resource for a variety of quantum information protocols. In this paper, we show the existence of AME states for any number of parties, given that the dimension of the involved systems is chosen appropriately. We prove the equivalence of AME states shared between an even number of parties and pure state threshold quantum secret sharing (QSS) schemes, and prove necessary and sufficient entanglement properties for a wider class of ramp QSS schemes. We further show how AME states can be used as a valuable resource for open-destination teleportation protocols and to what extend entanglement swapping generalizes to AME states