Erratum: “Description of rank four entangled states of two qutrits having positive partial transpose” [J. Math. Phys. 52, 122203 (2011)]

2012 ◽  
Vol 53 (7) ◽  
pp. 079903 ◽  
Author(s):  
Lin Chen ◽  
Dragomir Ž Đoković
Keyword(s):  
Entangled States ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Math Phys

scholarly journals Bound entanglement and distillability of multipartite quantum systems

2015 ◽  
Vol 13 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Hui Zhao ◽  
Xin-Yu Yu ◽  
Naihuan Jing
Keyword(s):  
Quantum Systems ◽  
Entangled States ◽  
Multipartite Quantum Systems ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Bound Entanglement

We construct a class of entangled states in ℋ = ℋA ⊗ ℋB ⊗ ℋC quantum systems with dim ℋA = dim ℋB = dim ℋC = 2 and classify those states with respect to their distillability properties. The states are bound entanglement for the bipartite split (AB) - C. The states are non-positive partial transpose (NPT) entanglement and 1-copy undistillable for the bipartite splits A - (BC) and B - (AC). Moreover, we generalize the results of 2 ⊗ 2 ⊗ 2 systems to the case of 2n ⊗ 2n ⊗ 2n systems.

scholarly journals Small sets of locally indistinguishable orthogonal maximally entangled states

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1098-1106
Author(s):  
Alessandro Cosentino ◽  
Vincent Russo
Keyword(s):  
Affirmative Answer ◽  
Semidefinite Program ◽  
Entangled States ◽  
Classical Communication ◽  
Fundamental Interest ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Maximally Entangled States ◽  
First Time

We study the problem of distinguishing quantum states using local operations and classical communication (LOCC). A question of fundamental interest is whether there exist sets of $k \leq d$ orthogonal maximally entangled states in $\complex^{d}\otimes\complex^{d}$ that are not perfectly distinguishable by LOCC. A recent result by Yu, Duan, and Ying [Phys. Rev. Lett. 109 020506 (2012)] gives an affirmative answer for the case $k = d$. We give, for the first time, a proof that such sets of states indeed exist even in the case $k < d$. Our result is constructive and holds for an even wider class of operations known as positive-partial-transpose measurements (PPT). The proof uses the characterization of the PPT-distinguishability problem as a semidefinite program.

scholarly journals Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 685
Author(s):  
Arunava Majumder ◽  
Harshank Shrotriya ◽  
Leong-Chuan Kwek
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Heisenberg Uncertainty Principle ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Heisenberg Uncertainty ◽  
Noise Limit ◽  
Entangled Quantum States ◽  
Standard Precision ◽  
Shot Noise Limit

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ `quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.

ENTANGLEMENT OF CONVEX LINEAR COMBINATION AND CONSTRUCTION OF PPT ENTANGLED STATES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350002 ◽  
Author(s):  
WEI CHENG ◽  
FANG XU ◽  
HUA LI ◽  
GANG WANG
Keyword(s):  
Linear Combination ◽  
Quantum States ◽  
Entangled States ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Convex Linear Combination ◽  
Ppt Criterion

Given two bipartite quantum states and the convex linear combination of them, we discuss the relation between the entanglement of the convex linear combination state and the entanglement of states being combined. This is achieved by characterizing quantum states quantitatively via the positive partial transpose (PPT) criterion and the computable cross-norm or realignment (CCNR) criterion. Inspired by the Horodecki's 3 ⊗ 3 quantum states, we also give explicit examples to illustrate all possible cases of convex linear combination. Finally, as an application of this method, we show how to construct new bipartite PPT entangled states from known PPT entangled states by convex linear combination.

scholarly journals Entanglement distillation by extendible maps

2013 ◽  
Vol 13 (9&10) ◽  
pp. 751-770
Author(s):  
Lukasz Pankowski ◽  
Fernando G.S.L. Brandao ◽  
Michal Horodecki ◽  
Graeme Smith
Keyword(s):  
The State ◽  
Entangled States ◽  
Classical Communication ◽  
Positive Partial Transpose ◽  
Epr Pairs ◽  
Numerical Studies ◽  
Partial Transpose ◽  
Maximally Entangled States ◽  
Werner States ◽  
Open Question

It is known that from entangled states that have positive partial transpose it is not possible to distill maximally entangled states by local operations and classical communication (LOCC). A long-standing open question is whether maximally entangled states can be distilled from every state with a non-positive partial transpose. In this paper we study a possible approach to the question consisting of enlarging the class of operations allowed. Namely, instead of LOCC operations we consider $k$-extendible operations, defined as maps whose Choi-Jamio\l{}kowski state is $k$-extendible. We find that this class is unexpectedly powerful - e.g. it is capable of distilling EPR pairs even from completely product states. We also perform numerical studies of distillation of Werner states by those maps, which show that if we raise the extension index $k$ simultaneously with the number of copies of the state, then the class of $k$-extendible operations are not that powerful anymore and provide a better approximation to the set of LOCC operations.

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