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Recently, the correspondence between the air track scenario and quantum database search algorithm was revealed. The conservation laws of linear momentum and nonlinear kinetic energy in the former case, which involve sequential elastic collisions, have their analogs in the latter case. Obviously, probability normalization combined with the Born rule serves as an analog for kinetic energy conservation. Here we explore the linear conservation laws in a generic quantum database search. Regarding the non-uniform distribution of the marked state, the uneven state is initially prepared. In this way, the Grover diffusion operator results in a linear but nonphysical conservation law. On the other hand, in the CTC-assisted database search with the vast reduction of query complexity, the nonlinear instead of linear conservation laws are found. Finally, we conjecture that there are no conservation laws in the generalized Grover’s algorithm including the imaginary number i. [ABSTRACT FROM AUTHOR]

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics. [ABSTRACT FROM AUTHOR]

We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, we introduce the notion of hybrid nonlocality distillation, in which different nonlocal boxes are exploited for nonlocality distillation. Here, we quantify the nonlocality using the violation degree of either the Clauser–Horne–Shimony–Holt inequality or the inequality. Our study shows that hybrid nonlocality distillation can outperform nonlocality distillation using copies of single nonlocal boxes. In particular, more nonlocality of undistillable boxes can be activated with the assistance of distillable boxes. Equivalently, distillable boxes can achieve more nonlocality with the assistance of undistillable boxes. [Copyright &y& Elsevier]

We present a proposal of the quantum secret encryption, transmission, and decryption implementation for quantum secret-sharing protocol using cavity QED. In the proposed scheme, the information is stored in two identical two-level atoms, and the two-qubit logic transformation is realized through the interaction between atoms and a nonresonant cavity mode. The proposed scheme requires no ancilla states to assist the intermediate atomic transitions and conditional quantum dynamics for quantum phase flip and quantum state diffusion. The encryption and decryption of quantum states are mostly governed by the Hamiltonian of an atom-cavity system. Moreover, secret transmission using quasi-swap gates for entanglement swapping has also been presented. With fewer supplements of external fields, a speed quantum protocol can be realized without universal gates. [ABSTRACT FROM AUTHOR]

The joint measurement approach has been shown to detect more information in quantum system. In this paper, we propose a quantum identification algorithm based on the joint quantum measurement. Through this, we can collectively compare an unknown quantum composite system with those in the database. In addition, this study will show that the proposed quantum algorithm can speed up the identification process quadratically. [ABSTRACT FROM AUTHOR]

Abstract: A physical n-input/n-output nonlocal machine is proposed for optimal values of Bell operators in the Bell-type inequalities. It is required that all outputs are locally random. In our scheme, maximally entangled ()-qubit GHZ states are employed for an n-input/n-output nonlocal machine. In addition, () bits of communication are necessary to avoid random correlation. We introduce how to perform quantum oblivious transfer using simulation of nonlocal machines. In addition, we also argue the security of quantum secret sharing using GHZ states are based on the nonlocal machines. [Copyright &y& Elsevier]

In this Letter, we consider the optimal probabilistic teleportation in N-level qudit via information extraction. We also argue that the purification scheme via entanglement swapping cannot achieve optimal efficiency in N-qubit case when N is larger than 2. [Copyright &y& Elsevier]

Abstract: We consider the loophole due to detector inefficiency in Cabello''s argument on Bell''s theorem without inequalities for the three-qubit system. It is shown that detectors with low efficiencies can be employed in physical tests. In addition, the mixed states due to the white noise are also considered. [Copyright &y& Elsevier]

Quantum Cheshire cats represent the violation of the product rule in terms of weak values being either 0 or 1. We explore the generalized fatter quantum Cheshire cats living in the larger Hilbert spaces. Specifically, two even-dimensional quantum systems are exploited. As for the physical implications, given that no disturbance is made in the weak measurements, quantum Cheshire cats reveal an alternative way of defying EPR elements of reality. In addition, we discuss the inconsistency between the Wigner's friend problem and quantum Cheshire cats. • We explore the quantum Cheshire cats in the Hilbert space of even-dimensions. • The EPR elements of reality can be refuted by quantum Cheshire cats. • The inconsistency between quantum Cheshire cats and Wigner's friend is studied. [ABSTRACT FROM AUTHOR]

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case. [ABSTRACT FROM AUTHOR]

We propose a scheme of entanglement purification via entanglement swapping. The scheme needs less classical communication to achieve the optimal purifying. We also prove that the optimal success probability is equal to the smaller entanglement of a single pair purification of these two pairs. [Copyright &y& Elsevier]

Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally entangled states in constructing EAQECCs is a practical obstacle to its use. It is also conjectured that the power of entanglement-assisted formalism to convert those good classical codes comes from massive consumption of maximally entangled states. We show that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length. Notably, two families of EAQECCs constructed in the paper require only one copy of maximally entangled state no matter how large the code length is. These families of EAQECCs that are constructed from classical finite geometric LDPC codes perform very well according to our numerical simulations. Our work indicates that EAQECCs are not only theoretically interesting, but also physically implementable. Finally, these high performance entanglement-assisted LDPC codes with low entanglement consumption rates allow one to construct high-performance standard QECCs with very similar parameters. [ABSTRACT FROM PUBLISHER]