NOTES ON THE FIDELITY OF SYMPLECTIC QUANTUM ERROR-CORRECTING CODES

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

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ac37e5 ◽

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.

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Environmental Effects on Nonlocal Correlations

Quanta ◽

10.12743/quanta.v8i1.86 ◽

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.

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