A procedure is developed to automatically correct the bit flip and the arbitrary phase change errors in Generalized Bell states (GBS). The phase and parity characteristics of the GBS are encoded in ancilla bits without altering the state under consideration. The same information is then used to correct the state at a different point, through appropriate unitrary control operations. It is also shown that the distributed/indirect measurements on ancilla can yield the error syndrome. The restricted error correction circuit obtained for N-qubit entangled states of the Bell type, are generalized for the corresponding higher dimensions, thus opening up the possibility of designing of task specific error correction circuits.
Experimental realization of automated error correction is demonstrated through IBM Quantum Experience for Bell and GHZ states using a measurement based approach upon ancilla qubits. The measurement automatically activates error correcting unitary operations to restore the system to its original entangled state. We illustrate the algorithm for the maximally entangled qudit case by applying appropriate Hadamard and Controlled-NOT gates.
Correlated photons produced by spontaneous parametric down-conversion are an essential tool for quantum communication, especially suited for long-distance connections. To have a reasonable count rate after all the losses in the propagation and the filters needed to improve the coherence, it is convenient to increase the intensity of the laser that pumps the non-linear crystal. By doing so, however, the importance of the four-photon component of the down-converted field increases, thus degrading the quality of two-photon interferences. In this paper, we present an easy derivation of this nuisan…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of the algorithms, thereby decreasing any quantum advantage. Here we present a task-specific error-correction technique that provides a complete protection over a restricted set of quantum states. Specifically, we give an automated error correction in Superdense Coding algorithms utilizing n-qubit generalized Bell states. At its core, it is based on non-destructi…
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations…
In 2007, and in a series of later papers, Joy Christian claimed to refute Bell's theorem, presenting an alleged local realistic model of the singlet correlations using techniques from Geometric Algebra (GA). Several authors published papers refuting his claims, and Christian's ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell's theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian …
A Simulation Framework for Noise and Error-Correction Analysis in Device-Independent Quantum Key Distribution
University of Information Technology, Ho Chi Minh City, Vietnam（胡志明市信息技术大学）；Vietnam National University, Ho Chi Minh City, Vietnam（胡志明市越南国立大学）；Faculty of Computer Science and Engineering, Thuyloi University, Hanoi, Vietnam（河内水利大学计算机科学与工程系）；Nara Institute of Science and Technology, Nara, Japan（日本奈良先端科学技术大学院大学）；Le Quy Don Technical University, Hanoi, Vietnam（河内黎贵敦技术大学）
A degree of violation of the Bell inequality depends on momenta of massive particles with respect to a laboratory if spin plays a role af a "yes--no" observable. For ultra-relativistic particles the standard Ekert test has to take into accont this velocity dependent suppression of the degree of violation of the inequality. Otherwise Alice and Bob may "discover" a nonexisting eavesdropper.
A quantum network is expected to enhance distributed quantum computing and quantum communication over a long distance while providing unconditional security. As quantum entanglement is essential for a quantum network, major issues from various types of noise and decoherence prevent it from being realized, and research has been intensively active to obtain optimal configurations for a quantum network. In this work, we address the performance of a quantum network capable of quantum error correction and entanglement purification. Our results show that one should distribute Bell pairs as fast as p…
We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by introducing additional drives and dissipation? The existence of autonomous quantum error correcting codes answers this question in the positive. Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overc…
We investigate the effects of error correction on non-local quantum coherence as a function of time, extending the study by Sainz and Björk. We consider error correction of amplitude damping, pure phase damping and combinations of amplitude and phase damping as they affect both fidelity and quantum entanglement. Initial two-qubit entanglement is encoded in arbitrary real superpositions of both Φ-type and Ψ-type Bell states. Our main focus is on the possibility of delay or prevention of ESD (early stage decoherence, or entanglement sudden death). We obtain the onset times for ESD as a function …
Automated discovery and optimization of autonomous quantum error correction codes for a general open quantum system
Advanced ICT Research Institute, National Institute of Information and Communications Technology（先进ICT研究所，信息与通信技术研究机构）；Research Institute for Science and Technology, Tokyo University of Science（理工学研究科，东京科学大学）
Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four different types of errors can occur on a qubit. Maximally entangled states are orthogonal to each other and hence can be uniquely distinguished by a measurement in the Bell basis. Thus a measurement in Bell basis and a unitary transformation is sufficient to correct error in Bell states. However, such a measurement is not possible for non-maximally entangled s…
Resource-adaptive distributed fault tolerance with very noisy Bell pairs
University of Bremen（不来梅大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；University of Oxford（牛津大学）；German Research Center for Artificial Intelligence GmbH（德国人工智能研究中心有限公司）
Remote entanglement of distant, non-interacting quantum entities is a key primitive for quantum information processing. We present a new protocol to remotely entangle two stationary qubits by first entangling them with propagating ancilla qubits and then performing a joint two-qubit measurement on the ancillas. Subsequently, single-qubit measurements are performed on each of the ancillas. We describe two continuous variable implementations of the protocol using propagating microwave modes. The first implementation uses propagating Schr$\rm{\ddot{o}}$dinger cat-states as the flying ancilla qubi…
Entanglement distribution is a core mechanism for the future quantum Internet. The quantum world is, however, a faulty environment. Hence, successful entanglement swapping is error-prone. The occurrence of quantum state errors can be mitigated using purification and error correction, which can be repeated in the former case and concatenated in the latter case. Repeated purification merges low-fidelity qubits into higher-quality ones, while concatenated error correction builds upon the redundancy of quantum information. In this article, we study in-depth and compare the two options: repeated pu…
