A. Fahmi | Searcharxiv

arXiv2015

Investigation of quantum entanglement simulation by random variables theories augmented by either classical communication or nonlocal effects

Bell's theorem states that quantum mechanics is not a locally causal theory. This state is often interpreted as nonlocality in quantum mechanics. Toner and Bacon [Phys. Rev. Lett. \textbf{91}, 187904 (2003)] have shown that a shared random-variables theory augmented by one bit of classical communication exactly simulates the Bell correlation in a singlet state. In this paper, we show that in Toner and Bacon protocol, one of the parties (Bob) can deduce another party's (Alice) measurement outputs, if she only informs Bob of one of her own outputs. Afterwards, we suggest a nonlocal version of Toner and Bacon protocol wherein classical communications is replaced by nonlocal effects, so that Alice's measurements cause instantaneous effects on Bob's outputs. In the nonlocal version of Toner and Bacon's protocol, we get the same result again. We also demonstrate that the same approach is applicable to Svozil's protocol.

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arXiv2008

Comment on "Quantum Key Distribution in the Holevo Limit"

In a Letter, Cabello proposed a quantum key distribution (QKD) Protocol which attended to Holevo limit. In this comment, we show that Eve could use a simple plan to distinguish among quantum keys, without being detected by Alice and Bob. In following, we show that our approach is not restricted to Cabello Protocol. With attention to our Eavesdropping approach, it seems that Mor's arguments for no-cloning principal for orthogonal states is not general enough to avoid eavesdropping.

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arXiv2007

Transition of D- Level Quantum Systems Through Quantum Channels with Correlated Noise

Entanglement and entanglement-assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this Paper, we study quantum-communication channels in $d$-dimensional systems and derive the mutual information of the quantum channels for maximally entangled states and product states coding with correlated noise. Then, we compare fidelity between these states. Our results show that there exists a certain fidelity memory threshold which depends on the dimension of the Hilbert space $(d)$ and the properties of noisy channels. We calculate the classical capacity of a particular correlated noisy channel and show that in order to achieve Holevo limit, we must use $d$ particles with $d$ degrees of freedom. Our results show that entanglement is a useful means to enhance the mutual information. We choose a special non-maximally entangled state and show that in the quasi-classical depolarizing and quantum depolarizing channels, maximum classical capacity in the higher memory channels is given by the maximally entangled state. Hence, our results show that for high error channels in every degree of memory, maximally entangled states have better mutual information.

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arXiv2006

Non-Locality and Classical Communication of the Hidden Variable Theories

In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature of quantum mechanics. In this paper, we derive Bell's inequality for particles with instantaneous interactions, and show that the aforementioned contradiction still exists between quantum mechanics and non-local hidden variable models. Then, we use this non-locality to obtain the GHZ theorem. In what follows, we show that Bacon and Toner's protocol, for the simulation of Bell correlation, by using local hidden variables augmented by classical communication, have some inconsistency with quantum mechanics. Our approach can answer to Brassard questions from another viewpoint, we show that if we accept that our nature obeys quantum mechanical laws, then all of quantum mechanic results cannot be simulated by realistic theories augmented by classical communication or a single instance use of non-local box.

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arXiv2006

Locality and the Greenberger-Horne-Zeilinger Theorem

In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature of quantum mechanics. In this Paper, we derive the Greenberger-Horne-Zeilinger type theorem for particles with instantaneous (non-local) interactions at the hidden-variable level. Then, we show that the previous contradiction still exists between quantum mechanics and non-local hidden variable models.

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arXiv2006

Entanglement-assisted Enhanced Information Transmission Over a Quantum Channel with Correlated Noise; A General Expression

Entanglement and entanglement-assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this paper, We study quantum communication channels with correlated noise and derive a general expression for the mutual information of quantum channel, for the product, maximally entangled state coding and entanglement-assisted systems with correlated noise in the Pauli quantum channels. Hence, we suggest more efficient coding in the entanglement-assisted systems for the transmission of classical information and derive a general expression for the entanglement-assisted classical capacity. Our results show that in the presence of memory, a higher amount of classical information is transmitted by two or four consecutive uses of entanglement-assisted systems.

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arXiv2006

New Approach to Quantum Key Distribution Via Quantum Encryption

In this Paper, we investigate the security of Zhang, Li and Guo quantum key distribution via quantum encryption protocol [$\text{Phys. Rev. A} \textbf{64}, 24302 (2001)$] and show that it is not secure against some of Eve's attacks and with the probability one half she gets all of keys without being detected by the two parties. The main defect in this protocol is that there is an attack strategy by which Eve can change the previously shared Bell state between Alice and Bob to two Bell states among herself and Alice and Bob. Hence, we show that with probability $1/d$ its generalization to $d$-dimension systems is not secure and show that its extension to the case of more partners based on the reusable GHZ states is not secure and with probability one half Eve gets all of keys without being detected by the two parties. In what follows, we show how in going to higher dimensions those protocols can be repaired.

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