Entanglement witnesses: construction, analysis and classification

Chruściński, Dariusz; Sarbicki, Gniewomir

doi:10.1088/1751-8113/47/48/483001

Cited by 185 publications

(188 citation statements)

References 190 publications

Supporting

Mentioning

182

Contrasting

Unclassified

Order By: Relevance

“…Here we will use the SDP for 'random robustness' [7] [20], this certification of causal nonseparability relies on a partial tomography of the process and thus requires trust in Alice's and Bob's local operations: it is 'devicedependent'.…”

Section: Causal Nonseparability and Causal Inequalitiesmentioning

confidence: 99%

Causally nonseparable processes admitting a causal model

2016

View full text Add to dashboard Cite

A recent framework of quantum theory with no global causal order predicts the existence of 'causally nonseparable' processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called 'causal inequalities' analogous to Bell inequalities) while others do not (they admit a 'causal model' analogous to a local model). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of 'white noise'. This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties.

show abstract

Section: Causal Nonseparability and Causal Inequalitiesmentioning

confidence: 99%

Causally nonseparable processes admitting a causal model

2016

View full text Add to dashboard Cite

show abstract

“…Example 1. The flip operator F is defined as F |φ ⊗ |ν = |ν ⊗ |φ [4]. After normalisation to unit trace we have W = 1 2 F = |φ + φ + | TB , where |φ + = 1 √ 2 (|00 + |11 ).…”

Section: Examples Of Entanglement Witnessesmentioning

confidence: 99%

“…Mathematically, the theory of entanglement witnesses gives a very nontrivial generalisation of positive semidefinite operators (for a recent review, see Ref. [4]). …”

Section: Introductionmentioning

confidence: 99%

Geometric representation of two-qubit entanglement witnesses

2015

View full text Add to dashboard Cite

Any two-qubit state can be represented geometrically by a steering ellipsoid inside the Bloch sphere. We extend this approach to represent any block positive two-qubit operator B. We derive a classification scheme based on the positivity of det B and det B T B ; this shows that any ellipsoid inside the Bloch sphere must represent either a two-qubit state or a two-qubit entanglement witness. We focus on such witnesses and their corresponding ellipsoids, finding that properties such as witness optimality are naturally manifest in this geometric representation.

show abstract

“…e is one that cannot be written as a convex combination of any two other block-negative operators, and hence, there exists a pure product state ja; bi ∈ S sep such that ha; bjŴ e ja; bi ¼ 0 [30,31]. We now introduce the set of extremal semiquantum witnessing games (ESQWGs), W e sq ⊂ W sq , which correspond to EEWs.…”

Section: An Extremal Ew (Eew)ŵmentioning

confidence: 99%

“…We now introduce the set of extremal semiquantum witnessing games (ESQWGs), W e sq ⊂ W sq , which correspond to EEWs. This class of games is necessary and sufficient for entanglement detection, since for every entangled state there exists an EEW which detects it [30,31] …”

Section: An Extremal Ew (Eew)ŵmentioning

confidence: 99%

Measurement-Device-Independent Approach to Entanglement Measures

2017

View full text Add to dashboard Cite

Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states. DOI: 10.1103/PhysRevLett.118.150505 Introduction.-Entanglement is a valuable resource for practical as well as fundamental applications of quantum theory, ranging from quantum computation and communication to metrology [1-3]. There are two major challenges in understanding entanglement that stimulates this research. First, it is extremely difficult to specify all the nonentangled bipartite or multipartite quantum states. In fact, the problem is known to be NP-hard [4,5]. Second, not surprisingly, the characterization of entangled states, i.e., the quantification of entanglement within quantum states, is an equally difficult task. The answer to the second challenge is practically very important because it tells us how well our protocols will perform using a given state [6][7][8][9].Focusing on the second challenge above, a first level of hardness is that the quantification of entanglement using almost any entanglement measure, e.g., entanglement of formation [10], negativity [11,12], or random robustness [13], requires estimating a large number of density matrix elements, a task which is difficult to perform on bipartite and multipartite quantum states. While this difficulty can be partially circumvented by making use of entanglement witnesses (EWs) when lower bounds on the entanglement are desired [14][15][16][17][18][19], errors and misalignments of the measurement devices can still lead to incorrect estimations of the quantities and thus, erroneous conclusions. A measurementdevice-independent approach is therefore desirable.Recent work by Buscemi [20] has introduced a new way to think about entanglement detection [21][22][23][24]. The idea is to map the problem onto a modified class of nonlocal games, called semiquantum nonlocal games (SQNLGs). In any such game, two players (Alice and Bob) share a possibly entangled state. A referee (Charlie) starts by asking them

show abstract

Entanglement witnesses: construction, analysis and classification

Cited by 185 publications

References 190 publications

Causally nonseparable processes admitting a causal model

Causally nonseparable processes admitting a causal model

Geometric representation of two-qubit entanglement witnesses

Measurement-Device-Independent Approach to Entanglement Measures

Contact Info

Product

Resources

About