Oleg Gittsovich

Covariance matrices and the separability problem.

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow us to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria--such as the computable cross-norm and local uncertainty criteria--as well as their limitations.

Unifying several separability conditions using the covariance matrix criterion

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We demonstrate that this criterion allows us to detect many states where the familiar criterion of the positivity of the partial transpose fails. It turns out that a large number of criteria that have been proposed to complement the positive partial transpose criterion\char22{}the computable cross norm or realignment criterion, the criterion based on local uncertainty relations, criteria derived from extensions of the realignment map, and others\char22{}are in fact a corollary of the covariance matrix criterion.

Steering bound entangled States: a counterexample to the stronger Peres conjecture.

Quantum correlations are at the heart of many applications in quantum information science and, at the same time, they form the basis for discussions about genuine quantum effects and their difference to classical physics. On one hand, entanglement theory provides the tools to quantify correlations in information processing and many results have been obtained to discriminate useful entanglement, which can be distilled to a pure form, from bound entanglement, being of limited use in many applications. On the other hand, for discriminating quantum phenomena from their classical counterparts, Schrödinger and Bell introduced the notions of steering and local hidden variable models. We provide a method to generate systematically bound entangled quantum states which can still be used for steering and, therefore, to rule out local hidden state models. This sheds light on the relations between the various views on quantum correlations and disproves a widespread conjecture known as the stronger Peres conjecture. For practical applications, it implies that even the weakest form of entanglement can be certified in a semidevice independent way.

Multiparticle covariance matrices and the impossibility of detecting graph-state entanglement with two-particle correlations

We present a criterion for multiparticle entanglement based on covariance matrices. On the one hand, the criterion allows detection of bound entangled states which are not detected by other criteria; on the other hand, some strongly entangled pure states such as the Greenberger-Horne-Zeilinger (GHZ) states are not detected. We show, however, that this is a general phenomenon: No separability criterion based on two-particle correlations can recognize the entanglement in the family of graph states to which the GHZ states belong.

Accessible nonlinear entanglement witnesses

(Dated: December 21, 2013)Verification of entanglement is an important tool to characterize sources and devices for use inquantum computing and communication applications. In a vast majority of experiments entangle-ment witnesses (EW) are used in order to prove the presence of entanglement in a quantum state.EWs can be constructed from available measurement results and do not require a reconstruction ofthe whole density matrix (full tomography), which is especially valuable for high-dimensional sys-tems. We provide a method to construct

Steering maps and their application to dimension-bounded steering

The existence of quantum correlations that allow one party to steer the quantum state of another party is a counterintuitive quantum effect that was described at the beginning of the past century. Steering occurs if entanglement can be proven even though the description of the measurements on one party is not known, while the other side is characterized. We introduce the concept of steering maps, which allow us to unlock sophisticated techniques that were developed in regular entanglement detection and to use them for certifying steerability. As an application, we show that this allows us to go beyond even the canonical steering scenario; it enables a generalized dimension-bounded steering where one only assumes the Hilbert space dimension on the characterized side, with no description of the measurements. Surprisingly, this does not weaken the detection strength of very symmetric scenarios that have recently been carried out in experiments.

Quantifying entanglement with covariance matrices

Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in terms of covariance matrices have been derived. We show how these results can be used for the quantification of entanglement in bipartite systems. To that aim we introduce an entanglement parameter that quantifies the violation of the covariance matrix criterion and can be used to give a lower bounds on the concurrence. These lower bounds are easily computable and give entanglement estimates for many weakly entangled states.

Gaussian-only regenerative stations cannot act as quantum repeaters

Higher transmission loss diminishes the performance of optical communication|be it the rate at which classical or quantum data can be sent reliably, or the secure key generation rate of quantum key distribution (QKD). Loss compounds with distance|exponentially in an optical fiber, and inverse-square with distance for a free-space channel. In order to boost classical communication rates over long distances, it is customary to introduce regenerative relays at intermediate points along the channel. It is therefore natural to speculate whether untended regenerative stations, such as phase-insensitive or phase-sensitive optical amplifiers, could serve as repeaters for long-distance QKD. The primary result of this paper rules out all bosonic Gaussian channels to be useful as QKD repeaters, which include phase-insensitive and phase-sensitive amplifiers as special cases, for any QKD protocol. We also delineate the conditions under which a Gaussian relay renders a lossy channel entanglement breaking, which in turn makes the channel useless for QKD.

Reliable Entanglement Verification

Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by Christandl and Renner [Phys. Rev. Lett. 109, 120403 (2012)] to construct a reliable entanglement verification procedure based on the concept of confidence regions. The statements made do not require the specification of a prior distribution, the assumption of independent measurements, or the assumption of an independent and identically distributed source of states. Moreover, we develop numerical tools that are necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this technique by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.

Role of correlations in the two-body-marginal problem

Quantum properties of correlations have a key role in disparate fields of physics, from quantum information processing, to quantum foundations, to strongly correlated systems. We tackle a specific aspect of the fundamental quantum marginal problem: we address the issue of deducing the global properties of correlations of tripartite quantum states based on the knowledge of their bipartite reductions, focusing on relating specific properties of bipartite correlations to global correlation properties. We prove that strictly classical bipartite correlations may still require global entanglement and that unentangled---albeit not strictly classical---reductions may require global genuine multipartite entanglement, rather than simple entanglement. On the other hand, for three qubits, the strict classicality of the bipartite reductions rules out the need for genuine multipartite entanglement. Our work sheds new light on the relation between local and global properties of quantum states, and on the interplay between classical and quantum properties of correlations.