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International Conference on Computing, Communication, and Intelligent Systems (ICCCIS)

Entanglement of Bell Diagonal States Induced by Quantum Channels

Varsha Sambhaje, Suprabhat Sinha, Anju Chaurasia

Published Nov 3, 2023• 1 citation
Publisher

Abstract

Bell states are special sets of entangled states that serve as a foundation for the corresponding Hilbert space. Being the maximally entangled states, they have significant importance in the field of quantum information theory. Among the mixed two-qubit state space, a highly intriguing limited class of states is the Bell diagonal states. Despite their inherent simplicity, Bell diagonal states exhibits a diverse range of correlations. In this paper, we explore the behaviour of Bell diagonal states under different quantum channels to pursue the geometrical illustration of quantum correlations leading to the entanglement. We propose the convex combination of distinct Bell states to prepare the Bell diagonal states. The whole class of Bell diagonal states is generated and entanglement is simulated throughout each parameter space and compared to the theory.

DOI
10.1109/icccis60361.2023.10425105

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Bell states are special sets of entangled states that serve as a foundation for the corresponding Hilbert space. Being the maximally entangled states, they have significant importance in the field of quantum information theory. Among the mixed two-qubit state space, a highly intriguing limited class of states is the Bell diagonal states. Despite their inherent simplicity, Bell diagonal states exhibits a diverse range of correlations. In this paper, we explore the behaviour of Bell diagonal states under different quantum channels to pursue the geometrical illustration of quantum correlations leading to the entanglement. We propose the convex combination of distinct Bell states to prepare the Bell diagonal states. The whole class of Bell diagonal states is generated and entanglement is simulated throughout each parameter space and compared to the theory.
Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as identical (equivalent, in fact, for pure two qubit states, that is, Gisin's Theorem ), yet they constitute different resources. Describing nonlocality by means of the violation of several Bell inequalities, we obtain by direct optimization those states of two qubits that maximally violate a Bell inequality, in terms of their degree of mixture as measured by either their participation ratio R = 1/Tr(ρ 2 ) or their maximum eigenvalue λ max . This optimum value is obtained as well, which coincides with previous results. Comparison with entanglement is performed too. An example of an application is given in the XY model. In this novel approximation, we also concentrate on the nonlocality for linear combinations of pure states of two qubits, providing a closed form for their maximal nonlocality measure. The case of Bell diagonal mixed states of two qubits is also extensively studied. Special attention concerning the connection between nonlocality and entanglement for mixed states of two qubits is paid to the so-called maximally entangled mixed states. Additional aspects for the case of two qubits are also described in detail. Since we deal with qubit systems, we will perform an analogous study for three qubits, employing similar tools. Relation between distillability and nonlocality is explored quantitatively for the whole space of states of three qubits. We finally extend our analysis to four-qubit systems, where nonlocality for generalized Greenberger–Horne–Zeilinger states of arbitrary number of parties is computed.
The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.
Abstract Entanglement and decoherence are two intimately related phenomena that lie at the heart of quantum information. The EPR-Bell states are the most basic quantum systems, which form the complete entangled basis of the two-particle Hilbert space, and which are important in many quantum computation schemes. The bit flip, phase flip, and bit-phase flip noise channels represent all the possible errors in quantum computation. Thus, the quantum decoherence characteristic of maximally and partially Bell entangled states under different noisy channels is studied using the concurrence. Our work is useful for linear-optical quantum computation and quantum communication schemes whose building blocks are entangled state.
Abstract Bell states are of crucial importance for entanglement based methods in quantum information science. Typically, a standard construction of a complete orthonormal Bell-basis by Weyl–Heisenberg operators is considered. We show that the group structure of these operators has strong implication on error correction schemes and on the entanglement structure within Bell-diagonal states. In particular, it implies an equivalence between a Pauli channel and a twirl channel. Interestingly, other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure, for instance in the share of positive partial transposition (PPT)-entangled states. In detail, we find that the standard Bell basis has the highest observed share on PPT-states and PPT-entangled states compared to other Bell bases. In summary, our findings show that the standard Bell basis construction exploits a very special structure with strong implications to quantum information theoretic protocols if a deviation is considered.
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In the field of quantum information and technology, entanglement in quantum systems called qudits is regarded as resource for quantum-based or quantum-assisted information processing tasks.It allows new ways of information processing like quantum computation or quantum teleportation and provides possibilities for speedups in a variety of algorithms with applications like search or optimization.Despite its theoretical and practical relevance, there is no general method to determine whether a given quantum state is entangled or not due to a special and hard to detect form of entanglement called bound entanglement.Bipartite Bell states are maximally entangled states of two qudits and are of high relevance for application in quantum technologies.Mixtures of those states can be entangled, including its bound form, or separable.Leveraging their special properties, Bell states can be numerically generated and analyzed for their entanglement properties by various methods implemented in this Julia package.