scholarly journals Construction of genuinely entangled subspacesand the associated bounds on entanglement measures for mixed states

2021 ◽  
Author(s):  
Konstantin Antipin
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Lower Bounds ◽  
Quantum Information Processing ◽  
Multipartite Entanglement ◽  
Quantum Channels ◽  
Valuable Resource ◽  
Mixed States ◽  
Entanglement Measures ◽  
Pure States

Abstract Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces — the class of subspaces consisting entirely of genuinely entangled pure states. In this paper we present methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the composition of bipartite entangled subspaces and quantum channels of certain types. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.

scholarly journals Coherent preorder of quantum states

2020 ◽  
Vol 20 (13&14) ◽  
pp. 1124-1137
Author(s):  
Zhaofang Bai ◽  
Shuanping Shuanping Du
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Coherent States ◽  
Quantum Coherence ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Mixed States ◽  
Quantum Hypothesis ◽  
Quantum Hypothesis Testing

As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with manipulation of families of quantum states rather than individual states in isolation. Given two pairs of coherent states $(\rho_1,\rho_2)$ and $(\sigma_1,\sigma_2)$, we are aimed to study how can we determine if there exists a strictly incoherent operation $\Phi$ such that $\Phi(\rho_i) =\sigma_i,i = 1,2$. This is also a classic question in quantum hypothesis testing. In this note, structural characterization of coherent preorder under strongly incoherent operations is provided. Basing on the characterization, we propose an approach to realize coherence distillation from rank-two mixed coherent states to $q$-level maximally coherent states. In addition, one scheme of coherence manipulation between rank-two mixed states is also presented.

scholarly journals Environmental Effects on Nonlocal Correlations

Quanta ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 57-67
Author(s):  
Tamal Guha ◽  
Bihalan Bhattacharya ◽  
Debarshi Das ◽  
Some Sankar Bhattacharya ◽  
Amit Mukherjee ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Classical Mechanics ◽  
Complete Loss ◽  
Quantum Channels ◽  
Output State ◽  
Environmental Interactions ◽  
Nonlocal Correlations

Environmental interactions are ubiquitous in practical instances of any quantum information processing protocol. The interaction results in depletion of various quantum resources and even complete loss in numerous situations. Nonlocality, which is one particular quantum resource marking a significant departure of quantum mechanics from classical mechanics, meets the same fate. In the present work we study the decay in nonlocality to the extent of the output state admitting a local hidden state model. Using some fundamental quantum channels we also demonstrate the complete decay in the resources in the purview of the Bell–Clauser–Horne–Shimony–Holt inequality and a three-settings steering inequality. We also obtain bounds on the parameter of the depolarizing map for which it becomes steerability breaking pertaining to a general class of two qubit states.Quanta 2019; 8: 57–67.

scholarly journals Characterizing entanglement and measurement’s uncertainty in neutrino oscillations

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Li-Juan Li ◽  
Fei Ming ◽  
Xue-Ke Song ◽  
Liu Ye ◽  
Dong Wang
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Neutrino Oscillations ◽  
Quantum Information Processing ◽  
Dynamical Evolution ◽  
Quantum Properties ◽  
Entanglement Measures ◽  
Potential Applications ◽  
Oscillation Process ◽  
Theoretical Results

AbstractSince neutrino oscillations (NOs) show nonclassical features with the Leggett–Garg inequality and exhibit potential applications in quantum information processing and telecommunications, in order to further reveal quantum properties of the NO systems, we herein focus on investigating entanglement and entropic uncertainty relation in the context of three-flavor NOs. Specifically, we take advantage of three different types of entanglement measures to characterize quantum resources originating from NO systems, and examine the hierarchical relationship among them. Moreover, we analyze the experiment data from different neutrino sources including Daya Bay (0.5 and 1.6 km) and MINOS+ (735 km) collaborations in comparison with our theoretical results. We find that the dynamical evolution of both the entropic uncertainty and entanglement of system shows non-monotonicity, and the experimental results coincide with our theoretical prediction very well. Interestingly, it shows that neutrinos always maintain quantum properties during oscillation process. More importantly, we reveal that the variation of the uncertainty is almost anti-correlated with that of the entanglement of system. Therefore, the nature of entanglement and uncertainty in NOs can be explored in the practical experiment when the three-flavor neutrino states are treated as three-qubit ones, which might be useful for the potential NO-based applications on prospective quantum information processing.

Correlations, Nonlocality and Usefulness of an Efficient Class of Two-Qubit Mixed Entangled States

2018 ◽  
Vol 73 (3) ◽  
pp. 191-206 ◽  
Author(s):  
Parvinder Singh ◽  
Atul Kumar
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Weak Measurement ◽  
Analytical Relation ◽  
Entangled States ◽  
Mixed States ◽  
New Class ◽  
Chsh Inequality ◽  
Noisy Conditions

AbstractWe establish an analytical relation between the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality and weak measurement strengths under noisy conditions. We show that the analytical results obtained in this article are of utmost importance for proposing a new class of two-qubit mixed states for quantum information processing. Our analysis further shows that the states proposed here are better resources for quantum information in comparison to other two-qubit mixed entangled states.

Multipartite entanglement and hyperdeterminants

2002 ◽  
Vol 2 (Special) ◽  
pp. 540-555
Author(s):  
A. Miyake ◽  
M. Wadati
Keyword(s):  
Entangled States ◽  
Multipartite Entanglement ◽  
Maximal Dimension ◽  
Ordered Structure ◽  
Mixed States ◽  
Separable States ◽  
Entanglement Measures ◽  
Pure States ◽  
Maximally Entangled States ◽  
Bipartite Case

We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the \(n \!\geq\! 4\) qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical \(n\)-partite entangled states. Our classification is also useful for that of mixed states.

scholarly journals NOTES ON THE FIDELITY OF SYMPLECTIC QUANTUM ERROR-CORRECTING CODES

2003 ◽  
Vol 01 (04) ◽  
pp. 443-463 ◽  
Author(s):  
MITSURU HAMADA
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Exponential Convergence ◽  
Error Correcting Codes ◽  
Quantum Channels ◽  
General Quantum ◽  
Quantum Capacity ◽  
Stabilizer Code ◽  
Quantum Error

Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the "probability" of the correctable errors for general quantum channels. The second observation states that for any coding rate below the quantum capacity, exponential convergence of the fidelity of some codes to unity is possible.

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