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arXiv:quant-ph/0107082 · Physical Review A

Classical analog of entanglement

Daniel Collins, Sandu Popescu

Published Feb 27, 2002• 86 citations
arXivHTMLPDF

Abstract

We show that quantum entanglement has a very close classical analog, namely, secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogies follow. In particular, teleportation is analogous to the one time pad, the concept of ``pure state'' exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single-copy-entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement, it allows one to identify those aspects of entanglement that are uniquely quantum mechanical.

DOI
10.1103/physreva.65.032321

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We show that quantum entanglement has a very close classical analog, namely, secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogies follow. In particular, teleportation is analogous to the one time pad, the concept of ``pure state'' exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single-copy-entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement, it allows one to identify those aspects of entanglement that are uniquely quantum mechanical.
In this Letter we study the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution p(XYZ) and transform secret bits back into p(XYZ) at equal rates using local operation and public communication. This is the classical analog to the well-studied problem of reversibly concentrating and diluting entanglement in a quantum state. We identify the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution, and it is possible that all reversible distributions have this form. These distributions are more general than what is obtained by simply constructing a classical analog to the family of quantum states known to have reversible entanglement. An indispensable tool used in our analysis is a conditional form of the Gács-Körner common information.
Abstract Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.
A counterintuitive result in entanglement theory was shown by Cubitt et al. [Phys. Rev. Lett. 91, 037902 (2003)], namely, that entanglement can be distributed by sending a separable state through a quantum channel. In this work, following an analogy between the entanglement and secret-key distillation scenarios, we derive its classical analog: secrecy can be distributed by sending nonsecret correlations through a private channel. This strengthens the close relation between entanglement and secrecy.
Entanglement is one of most peculiar characteristic of Quantum Mechanics (probably the other most mentioned is the particle tunneling through a barrier) because it entails correlations that supersedes classical correlations. It is conceived as the genuine quantum characteristic by many researchers and quite recently it has emerged as a physical resource to produce non-classical task, like quantum teleportation, quantum cryptography and quantum information. Entanglement could be distributed (efficient quantum communication is equivalent to efficient entanglement distribution (Plenio & Virmani, 2007)), concentrated (given an amount of entanglement, equal to the full content of entanglement in n pairs of identical entangled pure state systems, it is possible, using local operations on each system, to concentrate the total amount of entanglement into a smaller number m, m < n, of maximally pure entangled state system (Bennett, et al.; 1996)) and used to perform many quantum information tasks useful to overcome technical restrictions present on classical communication. In this chapter, we review the entanglement of quantum mechanical systems. First, in Section 2, we give a characterization of entanglement in terms of its special features as resource and its mathematical structure. Then, in section 3, we review some of the Bell inequalities. In Sections 4 and 5, we review some of the most important entanglement measures published for two and three entangled systems. After that, in Section 6, we give a characterization of quantum gates and operators by its entanglement power, i. e. the amount of entanglement that they can produce when acting on an arbitrary state. Finally, in Section 7, we briefly review the experimental detection of entanglement.
Quantum correlations have been an integral if sometimes discomforting aspect of quantum theory for over 85 years. From the early thought-experiments where they were used to argue that quantum mechanics was incomplete, through to their central position as resources in the modern theory of quantum information theory, quantum correlations have proved a hugely rich topic of study. This thesis explores a range of practical and foundational aspects within this ever developing field. Having reviewed fundamental material, we turn to consider the quantum correlations for a task termed anonymous metrology. This is used to demonstrate an operational distinction within the hierarchy of quantum correlations. Building from this we formulate the concept of quantum delocalised interactions, making use of quantum games to study the necessary correlations. With these we establish strong connections to the concurrence monotone and additionally a link with quantum teleportation. We then move to considering entanglement under motion when relativity is accounted for. We demonstrate how the entanglement between internal energy and motional states can be affected by boosts in an analogous way to the known behaviour for spins, and in a more straightforward manner. We then show how this understanding sheds light on the topic of proper time for quantum clocks. Finally we consider a protocol where entanglement can be used to witness non-classicality of gravity. We present improvements which help to bring the scheme closer to experimental feasibility, together with pointing out a potential loophole and how to close it.
Quantum entanglement is a key feature of quantum mechanics. It describes connections between quantum systems that classical theories cannot explain. The idea of entanglement started with the Einstein–Podolsky–Rosen (EPR) argument. This argument questioned whether quantum theory was complete and showed the non-classical nature of quantum correlations. Schrödinger later defined the concept and introduced the term "entanglement" to describe composite quantum states that cannot be separated. Bell then created a framework that showed the predictions of quantum mechanics clash with local hidden-variable theories, leading to Bell's inequality. Experiments by Aspect and others provided strong evidence for the violation of Bell's inequalities and supported the reality of entanglement. Building on these theories and experiments, quantum teleportation became an important protocol in quantum information science. Bennett and his team proposed a scheme that showed how an unknown quantum state can be sent between distant parties using shared entanglement and classical communication, without sending the quantum system itself. Later experiments confirmed that this protocol works across different physical platforms. This paper reviews the historical development of quantum entanglement and its role in the emergence of quantum teleportation. In addition to the theoretical discussion, the teleportation protocol is implemented using IBM's Qiskit framework. The simulation results demonstrate the successful transfer of quantum states within the circuit model, illustrating how fundamental quantum communication concepts can be explored using quantum computing simulation tools.