Universal detection of entanglement in two-qubit states using only two copies

Goswami, Suchetana; Chakraborty, Sagnik; Ghosh, Sibasish; Majumdar, A. S.

doi:10.1103/physreva.99.012327

Cited by 13 publications

(8 citation statements)

References 69 publications

(94 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(B6)). Thereafter, solving (15), and ( 16), we obtain q2 k and p2 k . In Appendix B, we compute q2 r and p2 r for a known displaced squeezed thermal state.…”

Section: Thereafter Estimating Q2mentioning

confidence: 99%

See 1 more Smart Citation

Detecting entanglement in arbitrary two-mode Gaussian state: a Stokes-like operator based approach

Dutta¹,

Ghosh²,

Jaewan³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Detection of entanglement in quantum states is one of the most important problems in quantum information processing. However, it is one of the most challenging tasks to find a universal scheme which is also desired to be optimal to detect entanglement for all states of a specific class-as always preferred by experimentalists. Although, the topic is well studied at least in case of lower dimensional compound systems, e.g., two-qubit systems, but in the case of continuous variable systems, this remains as an open problem. Even in the case of two-mode Gaussian states, the problem is not fully solved. In our work, we have tried to address this issue. At first, a limited number of Hermitian operators is given to test the necessary and sufficient criterion on the covariance matrix of separable two-mode Gaussian states. Thereafter, we present an interferometric scheme to test the same separability criterion in which the measurements are being done via Stokes-like operators. In such case, we consider only single-copy measurements on a two-mode Gaussian state at a time and the scheme amounts to the full state tomography. Although this latter approach is a linear optics based one, nevertheless it is not an economic scheme. Resource-wise a more economical scheme than the full state tomography is obtained if we consider measurements on two copies of the state at a time. However, optimality of the scheme is not yet known.

show abstract

“…(B6)). Thereafter, solving (15), and ( 16), we obtain q2 k and p2 k . In Appendix B, we compute q2 r and p2 r for a known displaced squeezed thermal state.…”

Section: Thereafter Estimating Q2mentioning

confidence: 99%

“…Using the notion of weak values, a resource-wise less demanding universal entanglement witnessing scheme (using two copies of the state at a time) for two qubits was proposed in Ref. [15], although it eventually amounts to state tomography. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Detecting entanglement in arbitrary two-mode Gaussian state: a Stokes-like operator based approach

Dutta¹,

Ghosh²,

Jaewan³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Also to quantify the amount of the same in a given system, there are several well studied measures for bipartite systems, such as negativity [12], concurrence [13,14] and many more [15,16]. While the field of detecting and measuring entanglement in bipartite system is a well explored area in quantum information theory [17][18][19][20][21], moving to more parties and/or higher dimensions are still much untraveled in the literature. In most of the realisations of quantum algorithms the systems under consideration are multipartite and hence motivates the community to deal with the properties of entanglement in such scenarios.…”

Section: Introductionmentioning

confidence: 99%

Detecting entanglement harnessing Lindblad structure

Chimalgi¹,

Bhattacharya²,

Goswami³

et al. 2022

Preprint

View full text Add to dashboard Cite

The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but noncompletely positive maps. Here we try to give a generic prescription to construct a positive map that can be useful for such scenarios. We study a class of positive maps arising from Lindblad structures. We show that two famous positive maps viz. transposition and Choi map can be obtained as a special case of a class of positive maps having Lindblad structure. Generalizing the transposition map to a one parameter family we have used it to detect genuine multipartite entanglement. Finally being motivated by the negativity of entanglement, we have defined a similar measure for genuine multipartite entanglement.

show abstract

“…It is seen that for these dimensions, all entangled states have negative partial transposition (NPT). There are different prescribed protocols for detection of two-qubit entanglement based on this criterion [11][12][13][14][15]. On the other hand, entanglement detection in general is a NP hard problem [16].…”

Section: Introductionmentioning

confidence: 99%

Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

Bhattacharya,

Goswami,

Mundra

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPTentangled state which is not detectable by certain other well-known entanglement detection criteria.

show abstract

Universal detection of entanglement in two-qubit states using only two copies

Cited by 13 publications

References 69 publications

Detecting entanglement in arbitrary two-mode Gaussian state: a Stokes-like operator based approach

Detecting entanglement in arbitrary two-mode Gaussian state: a Stokes-like operator based approach

Detecting entanglement harnessing Lindblad structure

Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

Contact Info

Product

Resources

About