DOCSLIB.ORG

Realization of the Tradeoff Between Internal and External Entanglement

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Realization of the Tradeoff Between Internal and External Entanglement PHYSICAL REVIEW RESEARCH 2, 043068 (2020) Realization of the tradeoff between internal and external entanglement Jie Zhu,1,3 Meng-Jun Hu,1,3 Yue Dai, 2,6 Yan-Kui Bai,4 S. Camalet,5 Chengjie Zhang,2,6,* Chuan-Feng Li,1,3 Guang-Can Guo,1,3 and Yong-Sheng Zhang1,3,† 1Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China 2School of Physical Science and Technology, Ningbo University, Ningbo 315211, China 3CAS Center for Excellence in Quantum Information and Quantum Physics, Hefei 230026, China 4College of Physics and Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang, Hebei 050024, China 5Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France 6School of Physical Science and Technology, Soochow University, Suzhou 215006, China (Received 9 January 2019; revised 20 August 2020; accepted 25 August 2020; published 13 October 2020) We experimentally realize the internal and external entanglement tradeoff, which is a kind of entanglement monogamy relation different from that usually discussed. Using a source of twin photons, we find that the external entanglement in the twin photons and the path-polarization internal entanglement of one photon limit each other. In the extreme case, when the internal state is maximally entangled, the external entanglement must be vanishing, which illustrates entanglement monogamy. Our results of the experiment coincide with the theoretical predictions and therefore provide a direct experimental observation of the internal and external entanglement monogamy relations. DOI: 10.1103/PhysRevResearch.2.043068 I. INTRODUCTION to Gaussian states. Moreover, other entanglement measures, such as the squashed entanglement [10,11], the negativity Entanglement monogamy is one of the most fundamental [12–15], and the squared entanglement of formation [16–18], properties for multipartite quantum states, which means that were also employed to derive the corresponding entanglement if two qubits, A and B, are maximally entangled, then A or B monogamy inequalities. On the other hand, many experimen- cannot be entangled with the third qubit C [1,2]. The quan- tal results on entanglement and nonlocality have also been titative entanglement monogamy inequality was first proved reported [44,45], including entanglement monogamy in exper- by Coffman, Kundu, and Wootters (CKW) for three-qubit iments [46,47]. states [3], Recently, new kinds of monogamy relations have been 2 + 2 2 , CA|B CA|C CA|BC (1) derived by Camalet [48–51], i.e., internal entanglement (or local quantum resource) and external entanglement have a where C2 denotes the squared concurrence for quantifying bi- tradeoff. The usually discussed entanglement monogamy in- partite entanglement [4]. From Eq. (1), one can easily find that equalities in Refs. [5–7,11–14,16–18] indicate the tradeoff there is a consequent tradeoff between the amount of entangle- relation between E(AB ) and E(AC ) (or its extension to the ment shared by qubits A and B and the entanglement shared N-partite case), where E is one kind of entanglement mea- by qubits A and C. For three-qubit pure states, the difference sure and AB and AC are reduced density matrices from a between the right-hand side and the left-hand side of Eq. (1)is three-qubit state. Unlike these previously derived inequalities, defined as the so-called “three-tangle” [3], which is a genuine Camalet has proposed a different entanglement monogamy three-qubit entanglement measure. After the CKW inequality, inequality [48]. This monogamy relation shows that the local several entanglement monogamy inequalities [5–41] and even resource can influence the entanglement between subsystems monogamy equalities [42,43] were introduced. Osborne and and other external systems. Besides there is no limitation Verstraete proved the CKW monogamy inequality for N-qubit about local resources, which can be entanglement between states [5]. In Refs. [6,7], the CKW inequality was generalized different degrees, entanglement between different particles of the subsystems, local coherence, and so on. Consider the tripartite quantum state A1A2B illustrated in Fig. 1, where A1 *[email protected] and A2 come from the same physical system, but have been †[email protected] encoded in different degrees of freedom, and B is encoded in another physical system. This inequality shows the tradeoff ˜ Published by the American Physical Society under the terms of the relation between the internal entanglement EA1|A2 and the ex- ˜ Creative Commons Attribution 4.0 International license. Further ternal entanglement EA1A2|B, where E and E are two different ˜ distribution of this work must maintain attribution to the author(s) but related entanglement measures, and EA1A2|B (EA1|A2 ) de- and the published article’s title, journal citation, and DOI. notes the entanglement of A1A2B ( A1A2 ) under the bipartition 2643-1564/2020/2(4)/043068(10) 043068-1 Published by the American Physical Society JIE ZHU et al. PHYSICAL REVIEW RESEARCH 2, 043068 (2020) between A1 and A2, the inequality (2) for a general three-qubit |ψ pure state A1A2B becomes + |ψ , EF ( A1A2 ) EF ( A1A2|B ) 1 (3) ˜ | = where the intraparticle entanglement EA1 A2 is EF ( A1A2 ) / + − 2 / H(1 2 1 C ( A1A2 ) 2), H is the binary entropy =− − − − = H(x): x log2 x (1 x)log2(1 x), and C( ) max{0,σ1 − σ2 − σ3 − σ4} is the concurrence of with {σi} ∗ being the square roots of eigenvalues of σy ⊗ σy σy ⊗ σy in decreasing order [4]. The external entanglement EA1A2|B is |ψ FIG. 1. For the tripartite quantum state A1A2B, the subsystems EF ( A1A2|B ), as defined by A and A are in the same physical system but they are encoded in 1 2 |ψ = − † EF ( A1A2|B ): 1 max EF (U A1A2U ) different degrees of freedom, and B is encoded in another physical U system. E˜ | and E | represent the internal entanglement be- A1 A2 A1A2 B = − { ,λ − λ − λ λ } , tween A1 and A2 and the external entanglement between A1A2 and B, 1 f (max 0 1 3 2 2 4 ) (4) respectively. where U√denotes the unitary operators of A, f (x):= / + − 2/ {λ } H(1 2 1 x 2), and i are the eigenvalues of A1A2 A1A2|B (A1|A2). The inequality holds whatever is the under- in nonascending order [48,53]. In Ref. [53], the maximum lying physical nature of the internal entanglement. It can be entanglement for a given spectrum {λi} measured by the neg- entanglement between two long-distance-separated particles, ativity and the relative entropy of entanglement have also two short-distance-separated particles, or even 2 degrees of been provided. Thus, one can obtain the inequality (2) with freedom of a single particle. This last kind of internal entan- the intraparticle entanglement measure being the negativ- glement is considered here and for precision we refer to it as ity and the relative entropy of entanglement as well (see intraparticle entanglement. Appendix A). Here we experimentally demonstrate the entanglement For simplicity, we first consider a class of three-qubit pure monogamy relation between the intraparticle and external states with one parameter φ as an example: entanglement, with a source of twin photons. As shown in |01+|10 Fig. 1, there are two qubits (the polarization qubit A1 and the |= cos φ|110+sin φ √ |1 . (5) path qubit A2) encoded in photon A, but only one qubit (the 2 A1A2B polarization qubit B) is encoded in photon B. We provide a BasedonEqs.(3) and (4), one can obtain its intraparticle direct experimental observation of the tradeoff between the and external entanglement by using the entanglement of for- | 2 intraparticle entanglement in A1 A2 and the external entangle- mation, i.e., E ( ) = f (sin φ) and E (|ψ | ) = 1 − | F A1A2 F A1A2 B ment in A1A2 B. f (max{cos2 φ,sin2 φ}). Moreover, the states such as 1 cos θ|01+sin θ|10 II. THEORETICAL FRAMEWORK |= √ |110+ √ |1 (6) 2 2 A1A2B Let us focus on the tripartite state , where A and A A1A2B 1 2 = are also analyzed. For these states, we find EF ( A1A2 ) are encoded in the same physical system A by using different 1 f ( sin 2θ ), which depends on θ, and E (|ψ | ) = 1 − degrees of freedom (see Fig. 1). The third party is encoded in 2 F A1A2 B / ≈ . system B. Camalet’s entanglement monogamy inequality is f (1 2) 0 645 is a constant. The theoretical results are shown in Fig. 2 as the solid and dotted lines. We can see ˜ + ˜ , EA1|A2 EA1A2|B Emax (2) that all the results are bounded by the green dashed line, i.e., the monogamy inequality (3) always holds. Moreover, ˜ | where EA1 A2 denotes the intraparticle entanglement measure the inequality (3) is valid for any finite-dimensional subsys- | between A1 and A2, EA1A2 B is the external entanglement mea- tems. However, not all the general allowed region can be ˜ ˜ | sure between A1A2 and B, and Emax is the value of EA1 A2 when reached with three-qubit states. For all the three-qubit pure A1 and A2 are maximally entangled [48]. It is worth noting that states, since λ1 1/2 and there are at most only two nonzero E˜ and E are strongly related, although they are two different {λ ,λ } = − { ,λ } eigenvalues 1 2 for A1A2 , EF 1 f (max 0 1 ) entanglement measures. From the inequality (2), one can see 1 − f (1/2) ≈ 0.645, and this bound also holds for all three- | ˜ that EA1A2 B is also bounded by Emax. When the state A1A2B qubit mixed states. Therefore, the allowed region specific to is pure and the reduced density operator A1A2 is absolutely all three-qubit states is given in Fig.
Load more

Recommended publications
  • A Paradox Regarding Monogamy of Entanglement
    A paradox regarding monogamy of entanglement Anna Karlsson1;2 1Institute for Advanced Study, School of Natural Sciences 1 Einstein Drive, Princeton, NJ 08540, USA 2Division of Theoretical Physics, Department of Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden Abstract In density matrix theory, entanglement is monogamous. However, we show that qubits can be arbitrarily entangled in a different, recently constructed model of qubit entanglement [1]. We illustrate the differences between these two models, analyse how the density matrix property of monogamy of entanglement originates in assumptions of classical correlations in the construc- tion of that model, and explain the counterexample to monogamy in the alternative model. We conclude that monogamy of entanglement is a theoretical assumption, not necessarily a phys- ical property, and discuss how contemporary theory relies on that assumption. The properties of entanglement entropy are very different in the two models — a priori, the entropy in the alternative model is classical. arXiv:1911.09226v2 [hep-th] 7 Feb 2020 Contents 1 Introduction 1 1.1 Indications of a presence of general entanglement . .2 1.2 Non-signalling and detection of general entanglement . .3 1.3 Summary and overview . .4 2 Analysis of the partial trace 5 3 A counterexample to monogamy of entanglement 5 4 Implications for entangled systems 7 A More details on the different correlation models 9 B Entropy in the orthogonal information model 11 C Correlations vs entanglement: a tolerance for deviations 14 1 Introduction The topic of this article is how to accurately model quantum correlations. In quantum theory, quan- tum systems are currently modelled by density matrices (ρ) and entanglement is recognized to be monogamous [2].
    [Show full text]
  • Do Black Holes Create Polyamory?
    Do black holes create polyamory? Andrzej Grudka1;4, Michael J. W. Hall2, Michał Horodecki3;4, Ryszard Horodecki3;4, Jonathan Oppenheim5, John A. Smolin6 1Faculty of Physics, Adam Mickiewicz University, 61-614 Pozna´n,Poland 2Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, QLD 4111, Australia 3Institute of Theoretical Physics and Astrophysics, University of Gda´nsk,Gda´nsk,Poland 4National Quantum Information Center of Gda´nsk,81–824 Sopot, Poland 5University College of London, Department of Physics & Astronomy, London, WC1E 6BT and London Interdisciplinary Network for Quantum Science and 6IBM T. J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, NY 10598 Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. In the latter case, one is violating the semi-classical causal structure of space, which is a strictly weaker implication than cloning or non-monogamy. This is because both cloning and non-monogamy also lead to a breakdown of the semi-classical causal structure. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system.
    [Show full text]
  • Firewalls and the Quantum Properties of Black Holes
    Firewalls and the Quantum Properties of Black Holes A thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science degree in Physics from the College of William and Mary by Dylan Louis Veyrat Advisor: Marc Sher Senior Research Coordinator: Gina Hoatson Date: May 10, 2015 1 Abstract With the proposal of black hole complementarity as a solution to the information paradox resulting from the existence of black holes, a new problem has become apparent. Complementarity requires a vio- lation of monogamy of entanglement that can be avoided in one of two ways: a violation of Einstein’s equivalence principle, or a reworking of Quantum Field Theory [1]. The existence of a barrier of high-energy quanta - or “firewall” - at the event horizon is the first of these two resolutions, and this paper aims to discuss it, for Schwarzschild as well as Kerr and Reissner-Nordstr¨omblack holes, and to compare it to alternate proposals. 1 Introduction, Hawking Radiation While black holes continue to present problems for the physical theories of today, quite a few steps have been made in the direction of understanding the physics describing them, and, consequently, in the direction of a consistent theory of quantum gravity. Two of the most central concepts in the effort to understand black holes are the black hole information paradox and the existence of Hawking radiation [2]. Perhaps the most apparent result of black holes (which are a consequence of general relativity) that disagrees with quantum principles is the possibility of information loss. Since the only possible direction in which to pass through the event horizon is in, toward the singularity, it would seem that information 2 entering a black hole could never be retrieved.
    [Show full text]
  • The QBIT Theory of Consciousness
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 August 2019 doi:10.20944/preprints201905.0352.v4 The QBIT theory of consciousness Majid Beshkar Tehran University of Medical Sciences [email protected] [email protected] Abstract The QBIT theory is an attempt toward solving the problem of consciousness based on empirical evidence provided by various scientific disciplines including quantum mechanics, biology, information theory, and thermodynamics. This theory formulates the problem of consciousness in the following four questions, and provides preliminary answers for each question: Question 1: What is the nature of qualia? Answer: A quale is a superdense pack of quantum information encoded in maximally entangled pure states. Question 2: How are qualia generated? Answer: When a pack of quantum information is compressed beyond a certain threshold, a quale is generated. Question 3: Why are qualia subjective? Answer: A quale is subjective because a pack of information encoded in maximally entangled pure states are essentially private and unshareable. Question 4: Why does a quale have a particular meaning? Answer: A pack of information within a cognitive system gradually obtains a particular meaning as it undergoes a progressive process of interpretation performed by an internal model installed in the system. This paper introduces the QBIT theory of consciousness, and explains its basic assumptions and conjectures. Keywords: Coherence; Compression; Computation; Consciousness; Entanglement; Free-energy principle; Generative model; Information; Qualia; Quantum; Representation 1 © 2019 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 August 2019 doi:10.20944/preprints201905.0352.v4 Introduction The problem of consciousness is one of the most difficult problems in biology, which has remained unresolved despite several decades of scientific research.
    [Show full text]
  • Symmetrized Persistency of Bell Correlations for Dicke States and GHZ-Based Mixtures: Studying the Limits of Monogamy
    Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures: Studying the limits of monogamy Marcin Wieśniak ( [email protected] ) University of Gdańsk Research Article Keywords: quantum correlations, Bell correlations, GHZ mixtures, Dicke states Posted Date: February 26th, 2021 DOI: https://doi.org/10.21203/rs.3.rs-241777/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Version of Record: A version of this preprint was published at Scientic Reports on July 12th, 2021. See the published version at https://doi.org/10.1038/s41598-021-93786-5. Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures: Studying the limits of monogamy. Marcin Wiesniak´ 1,2,* 1Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics,, University of Gdansk,´ 80-308 Gdansk,´ Poland 2International Centre for Theory of Quantum Techologies, University of Gdansk,´ 80-308 Gdansk,´ Poland *[email protected] ABSTRACT Quantum correlations, in particular those, which enable to violate a Bell inequality1, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.
    [Show full text]
  • Quantum Entanglement in the 21St Century
    Quantum entanglement in the 21 st century John Preskill The Quantum Century: 100 Years of the Bohr Atom 3 October 2013 My well-worn copy, bought in 1966 when I was 13. George Gamow, recalling Bohr’s Theoretical Physics Institute 1928-31: Bohr’s Institute quickly became the world center of quantum physics, and to paraphrase the old Romans, “all roads led to Blegdamsvej 17” … The popularity of the institute was due both to the genius of its director and his kind, one might say fatherly, heart … Almost every country in the world has physicists who proudly say: “I used to work with Bohr.” Thirty Years That Shook Physics , 1966, p. 51. George Gamow, recalling Bohr’s Theoretical Physics Institute 1928-31: Bohr, Fru Bohr, Casimir, and I were returning home from the farewell dinner for Oscar Klein on the occasion of his election as a university professor in his native Sweden. At that late hour the streets of the city were empty. On the way home we passed a bank building with walls of large cement blocks. At the corner of the building the crevices between the courses of the blocks were deep enough to give a toehold to a good alpinist. Casimir, an expert climber, scrambled up almost to the third floor. When Cas came down, Bohr, inexperienced as he was, went up to match the deed. When he was hanging precariously on the second-floor level, and Fru Bohr, Casimir, and I were anxiously watching his progress, two Copenhagen policeman approached from behind with their hands on their gun holsters.
    [Show full text]
  • Engineering of Entanglement and Spin State Transfer Via Quantum Chains
    www.nature.com/scientificreports OPEN Engineering of entanglement and spin state transfer via quantum chains of atomic spins at large Received: 19 April 2018 Accepted: 29 August 2018 separations Published: xx xx xxxx Dmitry I. Bazhanov1,2,3, Ilia N. Sivkov4 & Valeri S. Stepanyuk1 Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement. In diverse systems, long-range interactions between magnetic adatoms on surfaces were investigated both the- oretically and in experiments1–11. Indirect coupling can be mediated by surface and bulk electrons(RKKY), superexchange or can be of dipole-dipole origin.
    [Show full text]
  • Monogamy of Correlations Versus Monogamy of Entanglement
    Quantum Inf Process (2010) 9:273–294 DOI 10.1007/s11128-009-0161-6 Monogamy of correlations versus monogamy of entanglement M. P. Seevinck Received: 31 July 2009 / Accepted: 21 December 2009 / Published online: 16 January 2010 © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quan- tum entanglement and non-locality (i.e., correlations that violate Bell-type inequali- ties) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results and present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling corre- lations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entan- gled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell’s theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, and in this regard it is stressed that not all non-local correlations are monogamous. Keywords Quantum mechanics · Entanglement · Non-locality · Monogamy · No-signalling · Shareability · Cryptography M.
    [Show full text]
  • Generalised Monogamy Relation of Convex-Roof Extended Negativity In
    www.nature.com/scientificreports OPEN Generalised monogamy relation of convex-roof extended negativity in multi-level systems Received: 29 June 2016 Tian Tian, Yu Luo & Yongming Li Accepted: 19 October 2016 In this paper, we investigate the generalised monogamy inequalities of convex-roof extended Published: 18 November 2016 negativity (CREN) in multi-level systems. The generalised monogamy inequalities provide the upper and lower bounds of bipartite entanglement, which are obtained by using CREN and the CREN of assistance (CRENOA). Furthermore, we show that the CREN of multi-qubit pure states satisfies some monogamy relations. Additionally, we test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum and show that the generalised monogamy inequalities are satisfied in this case as well. Quantum entanglement is one of the most important physical resources in quantum information processing1–4. As distinguished from classical correlations, quantum entanglement cannot be freely shared among many objects. We call this important phenomenon of quantum entanglement monogamy5,6. The property of monogamy may be as fundamental as the no-cloning theorem7, which gives rise to structures of entanglement in multipartite settings8,9. Some monogamy inequalities have been studied to apply entanglement to more useful quantum infor- mation processing. The property of monogamy property has been considered in many areas of physics: it can be used to extract an estimate of the quantity of information about a secret key captured by an eavesdropper in quantum cryptography10,11, as well as the frustration effects observed in condensed matter physics12,13 and even black-hole physics14,15.
    [Show full text]
  • Quantum Cryptography: Key Distribution and Beyond
    Quantum Cryptography: Key Distribution and Beyond Akshata Shenoy-Hejamadi 1, Anirban Pathak 2 & Srikanth Radhakrishna 3 1 Group of Applied Physics, University of Geneva, Switzerland. E-mail: [email protected] 2 Jaypee Institute of Information Technology, Noida, India. E-mail: [email protected] 3 Poornaprajna Institute of Scientific Research, Bangalore, India. E-mail: [email protected] Editors: Subhash Kak, Tabish Qureshi & Danko Georgiev Article history: Submitted on December 21, 2016; Accepted on May 10, 2017; Published on June 18, 2017; Corrected on February 15, 2018. niquely among the sciences, quantum cryptog- in e-commerce today. RSA in today’s world is safe so raphy has driven both foundational research long as a scalable quantum computer remains unfeasible. Uas well as practical real-life applications. We However, ideally, we wish to guarantee cryptographic review the progress of quantum cryptography in the security that follows only from basic physics. This is the last decade, covering quantum key distribution and promise of quantum cryptography. other applications. In particular, note the recent report on a loophole-free Quanta 2017; 6: 1–47. test of Bell’s inequality [2], thereby conclusively veri- fying the existence of quantum nonlocality in Nature, 1 Introduction and also attesting to the advancement of experimental techniques to prepare, transmit, manipulate and measure Cryptography is the technique of concealing confiden- quantum information. Another direction in cryptography tial information using physical or mathematical means. is to provide practicable tools embracing experimental While cryptologists find newer methods to conceal a se- limitations, e.g. quantum key distribution with pulses cret, cryptanalysts devise powerful methods to compro- having mean photon number much larger than one [3].
    [Show full text]
  • Building a Quantum Engineering Undergraduate Program Abraham Asfaw, Alexandre Blais, Kenneth R
    1 Building a Quantum Engineering Undergraduate Program Abraham Asfaw, Alexandre Blais, Kenneth R. Brown, Jonathan Candelaria, Christopher Cantwell, Lincoln D. Carr, Joshua Combes, Dripto M. Debroy, John M. Donohue, Sophia E. Economou, Emily Edwards, Michael F. J. Fox, Steven M. Girvin, Alan Ho, Hilary M. Hurst, Zubin Jacob, Blake R. Johnson, Ezekiel Johnston-Halperin, Robert Joynt, Eliot Kapit, Judith Klein-Seetharaman, Martin Laforest, H. J. Lewandowski, Theresa W. Lynn, Corey Rae H. McRae, Celia Merzbacher, Spyridon Michalakis, Prineha Narang, William D. Oliver, Jens Palsberg, David P. Pappas, Michael G. Raymer, David J. Reilly, Mark Saffman, Thomas A. Searles, Jeffrey H. Shapiro, and Chandralekha Singh (Received, revised, accepted dates of manuscript.) This work was S. E. Economou is with the Department of Physics, Virginia Tech, partially supported by the U.S. National Science Foundation under Blacksburg, Virginia 24061, U.S.A. grant EEC-2110432. S. Girvin, T. A. Searles, and S. E. Economou E. Edwards is with the IQUIST, University of Illinois Urbana- were supported by the U.S. Department of Energy, Office of Science, Champaign, Urbana, IL 61801, U.S.A. National Quantum Information Science Research Centers, Co-design M. F. J. Fox and H. Lewandowski are with JILA, National Institute Center for Quantum Advantage (C2QA) under contract number DE- of Standards and Technology and the University of Colorado, Boulder, SC0012704. M. Raymer acknowledges support from the NSF Engi- CO 80309, U.S.A. and Department of Physics, University of Colorado neering Research Center for Quantum Networks (CQN), led by the Boulder, Boulder, CO 80309, U.S.A. University of Arizona under NSF grant number 1941583.
    [Show full text]
  • Jhep05(2021)062
    Published for SISSA by Springer Received: February 12, 2021 Accepted: April 12, 2021 Published: May 10, 2021 Probing Hawking radiation through capacity of JHEP05(2021)062 entanglement Kohki Kawabata,a Tatsuma Nishioka,b Yoshitaka Okuyamaa and Kento Watanabec aDepartment of Physics, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan bYukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan cCenter for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA 95616, U.S.A. E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We consider the capacity of entanglement in models related with the gravita- tional phase transitions. The capacity is labeled by the replica parameter which plays a similar role to the inverse temperature in thermodynamics. In the end of the world brane model of a radiating black hole the capacity has a peak around the Page time indicating the phase transition between replica wormhole geometries of different types of topology. Similarly, in a moving mirror model describing Hawking radiation the capacity typically shows a discontinuity when the dominant saddle switches between two phases, which can be seen as a formation of island regions. In either case we find the capacity can be an invaluable diagnostic for a black hole evaporation process. Keywords: 2D Gravity, Black Holes ArXiv ePrint: 2102.02425 Open Access, c The Authors. https://doi.org/10.1007/JHEP05(2021)062 Article funded by SCOAP3.
    [Show full text]