Quantum stretching is a technique to make quasi-copies of an arbitrary qubit without violating the No-Cloning Theorem. These quasi-copies of the original qubit contain all the information of the original but at the cost of duplication in its size each time the technique is applied. Basically, a stretched bit or subit is obtained applying a single, unitary and reversible gate, i.e., we can recover the original qubit from its subit. Quantum stretching will allow us simultaneous teleportation to multiple destinations of the same subit, with the consequent potential that this has for quantum internet in configurations from 1 to N, however, always taking into account the duplication of qubit size to be quasi-copied every time the technique is applied. Finally, quantum stretching is particularly useful to make satellite bifurcations in the quantum internet context.
Quantum stretching is a technique to make quasi-copies of an arbitrary qubit without violating the No-Cloning Theorem. These quasi-copies of the original qubit contain all the information of the original but at the cost of duplication in its size each time the technique is applied. Basically, a stretched bit or subit is obtained applying a single, unitary and reversible gate, i.e., we can recover the original qubit from its subit. Quantum stretching will allow us simultaneous teleportation to multiple destinations of the same subit, with the consequent potential that this has for quantum internet in configurations from 1 to N, however, always taking into account the duplication of qubit size to be quasi-copied every time the technique is applied. Finally, quantum stretching is particularly useful to make satellite bifurcations in the quantum internet context.
Abstract One interesting application of entanglement is quantum teleportation, which is a technique for transferring an unknown quantum state from one place to another. In science fiction, teleportation generally involves a machine scanning a person and another machine reassembling the person on the other end. The original body disintegrates and no longer exists. Similarly, quantum teleportation works by “scanning” the original qubit, sending a recipe, and reconstructing the qubit elsewhere. The original qubit is not physically destroyed in the science fiction sense, but it is no longer in the same state. Otherwise, the previously mentioned no-cloning theorem—which states that a qubit cannot be exactly copied onto another qubit—would be violated.1 As we will see, the “scanning” part poses a problem which can only be solved by leveraging quantum entanglement.
Quantum internet, which is expected to be a combination of quantum and classical networks, promises to provide information-theoretic security for data exchange. Classical networks have well-established protocols for reliable end-to-end transmission that implicitly make use of duplicating classical bits. However, quantum bits (qubits) cannot be copied due to the no-cloning theorem. In this paper, we take advantage of the principle of creating imperfect clones using a Universal Quantum Copying Machine (UQCM) and propose the Quantum Automatic Repeat Request (QARQ) protocol, inspired by its classical equivalent. A simulation platform has been developed to study the feasibility of QARQ. Results show that our proposal is well suited for applications that are compatible with low fidelity requirements.
The Quantum Internet, a network interconnecting remote quantum devices through quantum links in synergy with classical ones, is envisioned as the final stage of the quantum revolution, opening fundamentally new communications and computing capabilities. But the Quantum Internet is governed by the laws of quantum mechanics. Phenomena with no counterpart in classical networks, such as no-cloning, quantum measurement, entanglement and quantum teleportation, impose new challenging constraints for network design. Specifically, classical network functionalities are based on the assumption that classical information can be safely read and copied. However, this assumption does not hold in the Quantum Internet. As a consequence, its design requires a major network-paradigm shift to harness the quantum mechanics specificities. The goal of this work is to shed light on the challenges and open problems of Quantum Internet design. We first introduce some basic knowledge of quantum mechanics, needed to understand the differences between a classical and a quantum network. Then, we introduce quantum teleportation as the key strategy for transmitting quantum information without physically transferring the particle that stores the quantum information or violating the principles of quantum mechanics. Finally, the key research challenges to design quantum communication networks are discussed.
Abstract One of the most important properties of quantum information, and the one ultimately responsible for its cryptographic applications, is that it can not be copied. That statement, however, is not completely accurate. While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. We fully characterize which regions of spacetime can all hold the same quantum information. Because quantum information can be delocalized through quantum error correction and teleportation, it need not follow well-defined trajectories. Instead, replication of the information in any configuration of spacetime regions not leading to violations of causality or the no-cloning principle is allowed. To demonstrate this, we answer the operational question of exactly when the information can be summoned to a set of spacetime points, showing how to do so efficiently using a combination of teleportation and codeword-stabilized quantum codes. This provides a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities.
Due to the Heisemberg uncertainty principle, it is impossible to design a procedure which permits perfect cloning of an arbitrary, unknown "qubit" (the spin or polarization state of a single quantum system)1,2. However, it is believed that a perfect copying protocol can be achieved, at least in principle, if the qubit to be copied is destroyed in the original system. Quantum teleportation3,4 is supposed to allow for such a result. Here, this belief is shown to be invalidated by a fundamental uncertainty about the number of particles involved in any process, as predicted by Quantum Field Theory. As a result, teleportation cannot provide an infallible copying procedure for the single qubits, not even in the limit of perfect experimental sensitivities. The no-cloning theorem1,2 can then be generalized to the case of destroying the original. Teleportation remains an interesting statistical procedure, having an unavoidable theoretical error at the percent level or few orders of magnitude smaller, depending on the physical process that is used. Although it cannot be made arbitrarily small, such an error is small enough to remain hidden in present experiments.
Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O(M/N 2), where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i) an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii) a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N 2, and iii) a protocol that generates O(N 2) nearly perfect copies of a generic pure state U |0〉 while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M 2/N 2.