Which verification qubits perform best for secure communication in noisy channel?

In secure quantum communication protocols, a set of single qubits prepared using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$) entangled states of a particular form are usually used to form a verification string which is subsequently used to detect traces of eavesdropping. The qubits that form a verification string are referred to as decoy qubits, and there exists a large set of different quantum states that can be used as decoy qubits. In the absence of noise, any choice of decoy qubits provides equivalent security. In this paper, we examine such equivalence for noisy environment (e.g., in amplitude damping, phase damping, collective dephasing and collective rotation noise channels) by comparing the decoy-qubit assisted schemes of secure quantum communication that use single qubit states as decoy qubits with the schemes that use entangled states as decoy qubits. Our study reveals that the single qubit assisted scheme perform better in some noisy environments, while some entangled qubits assisted schemes perform better in other noisy environments. Specifically, single qubits assisted schemes perform better in amplitude damping and phase damping noisy channels, whereas a few Bell-state-based decoy schemes are found to perform better in the presence of the collective noise. Thus, if the kind of noise present in a communication channel (i.e., the characteristics of the channel) is known or measured, then the present study can provide the best choice of decoy qubits required for implementation of schemes of secure quantum communication through that channel.Comment: 11 pages, 4 figure

Kak's three-stage protocol of secure quantum communication revisited: Hitherto unknown strengths and weaknesses of the protocol

Kak's three-stage protocol for quantum key distribution is revisited with special focus on its hitherto unknown strengths and weaknesses. It is shown that this protocol can be used for secure direct quantum communication. Further, the implementability of this protocol in the realistic situation is analyzed by considering various Markovian noise models. It is found that the Kak's protocol and its variants in their original form can be implemented only in a restricted class of noisy channels, where the protocols can be transformed to corresponding protocols based on logical qubits in decoherence free subspace. Specifically, it is observed that Kak's protocol can be implemented in the presence of collective rotation and collective dephasing noise, but cannot be implemented in its original form in the presence of other types of noise, like amplitude damping and phase damping noise. Further, the performance of the protocol in the noisy environment is quantified by computing average fidelity under various noise models, and subsequently a set of preferred states for secure communication in noisy environment have also been identified.Comment: Kak's protocol is not suitable for quantum cryptography in presence of nois

Long-range big quantum-data transmission

We introduce an alternative type of quantum repeater for long-range quantum communication with improved scaling with the distance. We show that by employing hashing, a deterministic entanglement distillation protocol with one-way communication, one obtains a scalable scheme that allows one to reach arbitrary distances, with constant overhead in resources per repeater station, and ultrahigh rates. In practical terms, we show that also with moderate resources of a few hundred qubits at each repeater station, one can reach intercontinental distances. At the same time, a measurement-based implementation allows one to tolerate high loss, but also operational and memory errors of the order of several percent per qubit. This opens the way for long-distance communication of big quantum data.Comment: revised manuscript including new result

Measurement-Based Noiseless Linear Amplification for Quantum Communication

Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require advanced experimental techniques such as noiseless amplification. Recently it was shown that the benefits of noiseless amplification could be extracted by performing a post-selective filtering of the measurement record to improve the performance of quantum key distribution. We apply this protocol to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We measure an effective entangled resource stronger than that achievable by even a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime. The measurement-based noiseless linear amplifier offers two advantages over its physical counterpart: ease of implementation and near optimal probability of success. It should provide an effective and versatile tool for a broad class of entanglement-based quantum communication protocols.Comment: 7+3 pages, 5+1 figures, close to published versio

Beating the channel capacity limit for linear photonic superdense coding

Dense coding is arguably the protocol that launched the field of quantum communication. Today, however, more than a decade after its initial experimental realization, the channel capacity remains fundamentally limited as conceived for photons using linear elements. Bob can only send to Alice three of four potential messages owing to the impossibility of carrying out the deterministic discrimination of all four Bell states with linear optics, reducing the attainable channel capacity from 2 to log_2 3 \approx 1.585 bits. However, entanglement in an extra degree of freedom enables the complete and deterministic discrimination of all Bell states. Using pairs of photons simultaneously entangled in spin and orbital angular momentum, we demonstrate the quantum advantage of the ancillary entanglement. In particular, we describe a dense-coding experiment with the largest reported channel capacity and, to our knowledge, the first to break the conventional linear-optics threshold. Our encoding is suited for quantum communication without alignment and satellite communication.Comment: Letter: 6 pages, 4 figures. Supplementary Information: 4 pages, 1 figur

Squeezed state purification with linear optics and feed forward

A scheme for optimal and deterministic linear optical purification of mixed squeezed Gaussian states is proposed and experimentally demonstrated. The scheme requires only linear optical elements and homodyne detectors, and allows the balance between purification efficacy and squeezing degradation to be controlled. One particular choice of parameters gave a ten-fold reduction of the thermal noise with a corresponding squeezing degradation of only 11%. We prove optimality of the protocol, and show that it can be used to enhance the performance of quantum informational protocols such as dense coding and entanglement generation.Comment: 4 pages, 3 figure