Quantum-states-as-information meets Wigner's friend A comment on Hagar and Hemmo
孙昌璞 - 中国科学院理论物理研究所
CEV
Controlled Evolution
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中国科学院理论物理研究所
正功条件与热机效率
Measurement do not lead to entropy increase
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2. 固态量子计算与关联系统演化的动力学敏感性
Quan, Song, Liu, Zanardi, and Sun, Decay of Loschmidt Echo Enhanced by Quantum Criticality, Phys. Rev. Lett. 96, 140604 (2006)
3. 量子信息启发的未来量子器件
中国科学院理论物理研究所
量子信息载体的物理实现
Ion Traps, Photons Liquid NMR
Nuclear Spins in Semiconductors
相干性
可规模化
易控制
Cooper-pair box ，SQUID, Single Juction
约瑟芬森结
2002-2003年JJ Q-比特的相干性得到极大改进
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Quantum State
quibt原理
quibt原理
量子纠缠（quantum entanglement）是一种量子力学现象，当两个或多个量子系统相互纠缠时，它们的量子状态之间会产生强烈的依赖关系，这种依赖关系与距离无关，即无论它们相距多远，都会保持相互影响。
这种现象被称为“纠缠态”。
纠缠态的产生可以通过一些实验来验证，其中最著名的实验是EPR实验，即爱因斯坦-波多尔斯基-罗森实验。
该实验涉及到两个粒子A和B，它们被制备成纠缠态，然后被分开并放置在相距很远的两个地方。
当测量其中一个粒子时，另一个粒子的状态也会立即改变，无论它们相距多远。
这种现象被称为“量子非局域性”，它与经典物理学中的局域性相矛盾。
纠缠态在量子计算和量子通信中有重要的应用。
例如，在量子密钥分发中，可以使用纠缠态来确保通信双方之间的信息传输是安全的。
此外，纠缠态还可以用于实现量子并行性、量子计算中的某些算法和量子纠错码等。
总的来说，量子纠缠是量子力学中一个非常神奇的现象，它打破了经典物理学的许多基本概念，并开启了全新的研究和应用领域。
量子态保真度 传输
量子态保真度传输英文回答：Quantum state fidelity is a measure of how well a quantum system can preserve its initial state during transmission or manipulation. It quantifies the similarity between the transmitted state and the original state. The higher the fidelity, the closer the transmitted state is to the original state.In quantum information processing, maintaining high fidelity is crucial for the successful transmission and manipulation of quantum states. Any loss or distortion of the quantum state can lead to errors and degrade the performance of quantum algorithms and protocols.To achieve high fidelity, several factors need to be considered. First, the quality of the quantum system itself is important. This includes the coherence time, which determines how long the quantum state can be preservedbefore it decoheres due to interactions with the environment. Additionally, the level of control and precision in manipulating the quantum state is crucial.Second, the transmission channel plays a significant role in fidelity. Quantum states can be transmitted through various physical systems, such as photons, ions, or superconducting circuits. Each system has its own characteristics and challenges in terms of maintaining fidelity. For example, in the case of photons, losses and noise in the optical fibers or detectors can degrade the fidelity. In the case of superconducting circuits, unwanted interactions with the environment can cause decoherence and reduce fidelity.Third, error correction techniques can be employed to enhance fidelity. Quantum error correction codes can detect and correct errors that occur during transmission or manipulation. These codes use additional qubits to encode the information redundantly, allowing for error detection and correction. By using error correction, the fidelity of the transmitted state can be significantly improved.In summary, maintaining high fidelity in quantum state transmission is crucial for the successful implementation of quantum information processing tasks. It requires a combination of high-quality quantum systems, carefully designed transmission channels, and error correction techniques.中文回答：量子态保真度是衡量量子系统在传输或操作过程中保持初始状态的能力的指标。
量子科技的应用作文英语
量子科技的应用作文英语Exploring the Quantum Frontier: Applications of Quantum Technology。
In the vast landscape of technological advancement, one realm stands out as both mysterious and promising: quantum technology. Harnessing the peculiar behaviors of quantum mechanics, quantum technology has the potential to revolutionize various fields, from computing to communication and beyond. In this essay, we will delve into the fascinating world of quantum technology, exploring its applications and envisioning its impact on the future.Quantum Computing: Unlocking Unprecedented Power。
At the forefront of quantum technology lies quantum computing, a paradigm-shifting approach to computation. Traditional computers rely on binary bits, which can exist in one of two states: 0 or 1. In contrast, quantum computers leverage quantum bits, or qubits, which can existin multiple states simultaneously due to the principle of superposition. This allows quantum computers to perform vast numbers of calculations simultaneously, leading to exponential increases in processing power.One of the most promising applications of quantum computing is in the field of cryptography. Current encryption methods, such as RSA, rely on the difficulty of factoring large numbers to ensure security. However, quantum computers could theoretically break these encryption schemes in a fraction of the time it would take traditional computers. Conversely, quantum cryptography offers a new paradigm for secure communication, utilizing the principles of quantum mechanics to enable unhackable encryption keys.Quantum Communication: The Dawn of Unbreakable Encryption。
Quantum Information
and computer science were divorced at their foundations by a fundamental thesis, that algorithms—procedures for solving mathematical problems—could be distinguished independent of the physical world. The thesis holds that problems are, among other things, either easy or hard to solve, and such distinctions persist no matter what the physical nature of the computational machinery is, be it mechanical, electrical, optical or anyother. Astonishingly, however, discoveries in the last decade showed this equivalence does not extend to information processors which utilize quantum physics. By utilizing non-classical states of matter, quantum-mechanical machines can easily solve certain problems which are hard for classical processors. Moreover, this capabilitycan exist even in the presence of imperfections and noise.Isaac ChuangQuantum Information Joining the Foundations ofPhysics and Computer ScienceThis reunion of the two fields has generated significant surprises for physics and computer science. Here, I try to describe the ideas underlying this new scien-tific area, and how current experiments are racing to develop access to this new realm, known as quantum information.Easy and Hard—Cryptography and FactoringThe ease or difficultyof solving mathematical problems might seem a bit esoteric, but, in fact, it is immediately relevant to everyday modern life. In particular, the security of most bank transactions, including the integrity of ATM machines, hinges upon the apparentlyenormous difficultyof one mathematical problem. How this is accomplished is simple to understand if you’ve ever played with a puzzle box. Just as carpenters design wooden boxes that open onlywhen sliders are oper-ated in the right sequence, and just as watchmakers build intricate mechanical locks for safes, modern cryptographers craft mathematical problems which are hard to solve without the right key. This key is a password, a string of digits transmitted over electronic networks, which authenticates identities between sender and receiver and encrypts data between buyer and seller. Today, such puzzles safeguard electronic documents, secret communications and financial transactions, includ-ing most web-based electronic commerce.Nearly all such cryptography is based on the difficulty of one mathematical problem: finding the prime factors of an integer. W hat two numbers, when multi-plied, give 91? It is easy to verify that 7313=91, but finding these factors is a task so time-consuming for large numbers that it is deemed impractical. For example, what are the factors of 1207? Or of 12433159? Modern applications use numbers with more than 310 decimal digits, which are believed torequire at least billions of years to factor. Thus, I could secretly choose two prime numbers and anonymously advertise their product in the New York Times. Years later, I could authorita-tivelyestablish myself as the author of the advertisement byreveal-ing the secret factors. Other methods allow data to be encrypted using prime numbers;today, the importance of prime numbers is such that a U.S. Patent1has even been granted for a cryptosystem using two specific primes.The confidence in factoring as a good cryptographic prob-lem rests on two observations. First, it has a long history. Euclid studied the properties of prime numbers in the days of the Greeks. Indeed, the fact that any positive integer can be “Nearly all suchcryptography is basedon the difficulty of onemathematical problem:finding the prime factors of an integer.”uniquely represented as a product of primenumbers is the fundamental theorem ofarithmetic.Second, it is a fundamental tenet ofcomputer science, known as the ModernChurch-Turing thesis, that a hard mathe-matical problem remains hard no matter thephysical nature of a machine used to solveit. No lock, after all, is perfectly secure;MIT undergraduates are notorious for theirexpertise at appearing behind apparentlylocked doors (and for authoring the “MITGuide to Lock Picking,”floating aroundthe internet). And one is always wary of new technologies which break locks;for example, a mechanical lock can be X-rayedand the pins measured, to reproduce a master key. However, according to the Modern Church-Turing thesis, inde-pendent of the laws of physics, no better computing technology exists that can factor numbers much faster than electronic machines. At this point, physics re-enters the story. In 1984, to great surprise and acclaim around the world, Peter Shor 2announced his discovery of an algorithm to easily factor integers, using a computing machine based on quantum physics. This wasastonishing! If such a machine could be built, it would jeopardize the most widely used modern cryptosystem. And other hard mathematical problems might also be easily solved. But what is a quantum computer, and is it realistic? The Quantum ComputerAll computing machines must be realized as physical devices that obey the laws of physics. Indeed, the first computers were mechanical machines, which essen-tially used Newtonian mechanics to solve mathematical problems. During the last century, these were replaced by electronic machines, with semiconductor devices employing electromagnetism and charge transport (Maxwell’s and Boltzmann’s equations) for representing information and performing computations. Moreover,for the past forty years, the number of transistor switches per square inch in the most important semiconductor, silicon, has been doubling roughly every 18months—a phenomenon often referred to as Moore’s Law. If this trend continues unabated, by 2015transistors will be the size of single atoms and molecules. At that length scale, the classical laws of physics give way to quantum mechanics. That is the realm in which quantum computers operate.The unique properties of quantum states of matter give rise to the additional computational capabilities of quantum computers. Single atoms can represent infor-mation in the form of zeros and ones, for example, as ground and excited states of atoms. But quantum physics allows additional superposition states, that areFigure 1Graph giving some perspective on the state of some (but not all!) currentquantum computer implementations,in terms of complexity of task accomplished plotted versus number of quantum bits (“qubits”) realized.Quantum Computers Today C o m p l e x i t y 1234567Number of Quantum Bitssimultaneously partly ground and partly excited states. These are still “digital,”in that, when measured, the atom can be found to be in only one of the two states,but before the measurement they can be in both at once.Even stranger is the fact that two atoms can simultaneously be in a linked kind of superposition state, known as entanglement . For example, the two can be prepared in a superposition of both atoms being excited, and both atoms being in their ground states. This is a uniquely quantum state which has no classical analogue;when measured, both atoms are always found to be in the same state,which reflects a classical correlation, but this correlation persists beyond what is possible classically.Using such superpositions and entanglement, a quantum computer can in a sense evaluate a mathematical function simultaneouslyon all possible input values.The multiple simultaneous computational pathways can then be interfered to obtain the desired result. Shor’s quantum factoring algorithm cleverly causes construc-tive interference to occur such that the desired result, the factors of an integer, are amplified and successfully output after a short number of instructions. These include manyof the usual computer programming instructions, such as addition,multiplication and boolean logic, but there are also new “quantum gates,”such as the Hadamard gate, a kind of “square root of not ”gate that transforms a bit from zero to an equal superposition of zero and one. Shor’s algo-rithm can factor an L digit integer using approximately L 3instruc-tions, a tremendous improvement over the approximately 2L required by the best known classical algorithm.Beyond quantum factoring, new algorithms have recently been discovered, giving provable exponential speedups betweenclassical and quantum. Notably, Edward Farhi 3, Jeffrey Goldstone 4, and collaborators showed that there exist treestructures that quantum processors can walk through easily, but classical processors find hard to traverse.These and other results have overturned the Church-Turing thesis, at the foundations of computer science, whichviews algorithms as existing completely outside of the worldof physics. Such a picture cannot hold when computers operating using quantum mechanics can easily perform tasks that computers solely utilizing classical mechanics and electrodynamics cannot. For computer science, this has been a great surprise that is slowly but surely gaining broad acceptance. For physics, there is delight in realizing that quantum mechanics will now be taught to aspiring new computer science students. Reduction to PracticeWill you ever be able to buy a quantum information processor at your local computer store? After all, many models of computation have come and gone;only those which are physically realistic, and realizable, are interesting. Over the past decade since Shor’s discovery, a race has been developing to reduce these theories1/3“Even stranger is the fact that two atoms can simultaneously be in a linked kind of superposition state,known as E N T A N G L E M E N T .”continues on page 44Isaac Chuang: Quantum Informationcontinued from page 29to practice and to understand whether or not a large-scale quantum computer ispossible in principle. A wide varietyof physical systems (see Figure 1, p. 28) have beenconsidered as candidate implementations, including single photons and atoms,Cooper pairs in superconducting metallic boxes, phases in Josephson junctions, elec-trons floating on liquid helium, nitrogen vacancies in diamond, trapped ions andnuclear spins. Among these, nuclear spins in molecules, controlled with magneticresonance techniques, have been used to demonstrate Shor’s factoring algorithm.Current systems have been limited to just a handful of quantum bits, butfuture quantum information processing systems, with many more quantum bits,and even more complex sequences of operations, are widely expected to be real-ized. Recently, several groups around the world showed that superconductorqubit realizations could remain in superposition states for up to several hundrednanoseconds. Especially promising are atomic systems with cold, trapped ions andneutral atoms, because they are particularly well understood, cleanly controlledusing pulsed laser excitations and accessible at time scales within reach of labo-ratoryequipment. Recent ion trap experiments have demonstrated simple two, threeand four qubit computations and manipulations, including quantum teleporation.From Quantum Information to New PhysicsPerhaps an even greater surprise than the discovery of fast quantum algorithmsis the realization that such algorithms can retain their speed even in the presenceof imperfections and fundamental noise sources. Quantum states, in particular super-positions and entangled states, are actually well known for their fragility;whenmeasured, a wavefunction collapses, and nearly any interaction with an environ-ment leads to a partial measurement of the state. This effect, known as decoher-ence, makes quantum systems evolve rapidly towards stable, classical states. Forexample, an excited atom is unstable;it inevitably decays by spontaneous emissionto reach its ground state. Unchecked, decoherence prohibits quantum comput-ers from functioning well, or for very long.However, it turns out that techniques from the theory of information, origi-nating in Claude Shannon’s5seminal study of communication channels in 1948,allow information to be protected against errors, and these error correction tech-niques extend to protect quantum information as well.More importantly, we now understand how reliable quantum circuits can beconstructed from faulty quantum gates. Early in the days of computation, Johnvon Neumann6drew upon biology to deal with the unreliability of vacuum tubetransistors;he developed a theoryof how reliable automata could operate even withfaultyorgans, as long as their failure probabilitywas below a certain, constant thresh-old. His theory is, by and large, unemployed in modern digital computers, becauseof the high degree of reliabilityof metal-oxide semiconductor field effect transis-tors in silicon. But von Neumann’s theories of fault tolerance generalize beauti-fullyto the quantum world, and are fundamentallywhydigital quantum computerscan conceivably work reliably despite decoherence.These results, drawn from the dawn of computer science, hold fascinating impli-cations for the world of physics. They imply that a sufficiently well-engineered quantum system can stay in entangled superposition states indefinitely, requiring onlyoccasional correction. The scheme works much like a refrigerator, but what is being reduced is not the kinetic energyof the air in the refrigerator, but the entropy of a quantum state.Borrowing an analogyfrom W olfgang Ketterle7, let me observe that just as imag-inarycitizens of the sun would be amazed byice cream given the discoveryof refrig-eration, I have no doubt that in the future, we will be thrilled by the properties of long-lived, pure, entangled quantum states, “cold”preserved and manipulated by fault-tolerant quantum processors. Already, many new connections have emerged. For example, entangled states are useful for precision time keeping, and for increasing the accessible precision of certain measurements. And communicating entangled states allows secret information to be shared between parties.Quantum computation offers the potential for quickly solving certain math-ematical problems important in modern cryptosystems. Less immediately, but even more fundamentally, quantum information brings new ideas from computer science to physics, and from physics to computer science. I am certain this is a rich quest upon which we have only just begun.endnotes1. U.S. Patent number 5,373,360.2. Peter W. Shor, Morss Professor of Applied Mathematics, MIT.3. Edward Farhi, Professor of Physics and Director, MIT Center for Theoretical Physics.4. Jeffrey Goldstone, Cecil and Ida Green Professor of Physics, MIT.5. MIT Professor Emeritus Claude E. Shannon (1916–2001), known as the “father of modern digital communications and information theory.”[MIT News Office, February27, 2001.]6. John von Neumann (1903–1957), Professor of Mathematics, The Institute for Advanced Study, Princeton University.7. Wolfgang Ketterle, John D. MacArthur Professor of Physics, MIT, and 2001Nobel Laureate. isaac chuang, Associate Professor of Physics and Associate Professor of Media Arts and Sciences in the MIT Center for Bits and Atoms, is a pioneer in the field of quantum information science. His experimental realization of two, three, five and seven quantum bit quantum computers using nuclear spins in molecules provided the first laboratory demonstrations of many important quantum algorithms, including Shor’s quantum factoring algorithm. The error correction, algorithmic cooling and entanglement manipulation techniques he developed provide new ways to obtain complete quantum control over light and matter, and lay a foundation for possible large-scale quantum information processing systems.Chuang came to MIT in 2000 from IBM, where he was a research staff member. He received his doctorate in Electrical Engineering from Stanford University, where he was a Hertz Foundation Fellow. Chuang also holds one master and two bachelors degrees, in Physics and Electrical Engineering, from MIT, and was a postdoctoral fellow at Los Alamos National Laboratory and the University of California at Berkeley. He is the author, together with Michael Nielsen, of the textbook Quantum Computation and Quantum Information.。
量子通信流程
量子通信流程Quantum communication is a cutting-edge technology that has the potential to revolutionize the way we transmit and receive information. 量子通信是一种前沿技术，有可能彻底改变我们传输和接收信息的方式。
By leveraging the unique properties of quantum mechanics, such as superposition and entanglement, quantum communication promises to provide unprecedented levels of security and speed. 通过利用量子力学的独特性质，如叠加态和纠缠，量子通信承诺提供前所未有的安全性和速度。
In traditional communication systems, information is transmitted using electromagnetic waves, such as radio signals or microwaves. 在传统的通信系统中，信息是使用电磁波传输的，比如无线电信号或微波。
However, quantum communication relies on the principles of quantum mechanics to transmit information using quantum bits, or qubits, which can exist in multiple states simultaneously. 然而，量子通信依赖于量子力学的原理，使用量子比特或量子位（qubits）来传输信息，它可以同时存在于多个状态。
This allows for the creation of communication channels that are theoretically impossible to eavesdrop on, providing an unprecedented level of security for sensitive information. 这样可以创建理论上无法窃听的通信频道，为敏感信息提供了前所未有的安全性。
Quantum Cryptography for Secure Communication
Quantum Cryptography for Secure CommunicationQuantum cryptography is a cutting-edge technology that has the potential to revolutionize the way we secure our communication. With the increasing threat of cyber attacks and data breaches, the need for secure communication has never been more critical. Quantum cryptography offers a promising solution to this problem by leveraging the principles of quantum mechanics to create unbreakable encryption keys. However, like any new technology, quantum cryptography also comes with its own set of challenges and limitations.One of the key advantages of quantum cryptography is its ability to provide unconditional security. Unlike traditional encryption methods, which rely on complex mathematical algorithms that can be potentially broken by powerful computers, quantum cryptography is based on the fundamental laws of physics. This means that any attempt to eavesdrop on a quantum-encrypted communication would disrupt the quantum state of the transmitted photons, alerting the communicating parties to the presence of a security breach. As a result, quantum cryptography offers a level of security that is theoretically impossible to compromise, making it an attractive option for highly sensitive communications, such as government and military operations.In addition to its unparalleled security, quantum cryptography also offers the potential for long-distance secure communication. Traditional encryption methods are limited by the distance over which secure keys can be reliably exchanged, as the transmission of keys over long distances increases the risk of interception. Quantum cryptography, on the other hand, is not bound by the same limitations, thanks to the phenomenon of quantum entanglement. This allows for the creation of secure keys that can be distributed over long distances without the risk of interception, opening up new possibilities for global secure communication networks.Despite these promising advantages, quantum cryptography also faces several challenges that must be addressed before it can be widely adopted. One of the main challenges is the practical implementation of quantum key distribution (QKD) systems. While the theoretical principles of QKD have been well-established, developing practicalsystems that can reliably generate and distribute quantum keys in real-world conditions is a complex and costly endeavor. Current QKD systems are also vulnerable to various technical issues, such as photon loss and noise, which can degrade the quality of the quantum keys and compromise their security.Another challenge facing quantum cryptography is the lack of infrastructure to support its widespread adoption. Building a global quantum communication network would require significant investment in new technologies and infrastructure, including quantum satellites and ground-based quantum repeaters. Additionally, there is a shortage of skilled professionals with expertise in quantum cryptography, further hindering the development and deployment of quantum-secure communication systems.Furthermore, quantum cryptography also raises ethical and regulatory concerns that must be carefully considered. The unbreakable nature of quantum encryption keys means that they cannot be accessed by authorized third parties, such as law enforcement agencies conducting criminal investigations. This has sparked debates about the balance between individual privacy and national security, as well as the need for new legal frameworks to govern the use of quantum-secure communication technologies.In conclusion, quantum cryptography holds great promise for the future of secure communication, offering unparalleled security and the potential for long-distance secure communication. However, the practical challenges, infrastructure requirements, and ethical considerations surrounding its adoption must be carefully addressed. With continued research and investment, quantum cryptography has the potential to revolutionize the way we secure our communication in the digital age.。
2022年普通高等学校招生全国统一考试(北京卷)英语真题(原卷版)
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a rXiv:q uant-ph/051223v122D ec25“Quantum-states-as-information”meets Wigner’s friend:A comment on Hagar and Hemmo J.Finkelstein 1Department of Physics San Jos´e State University San Jos´e ,CA 95192,U.S.A Abstract This is a comment on the paper by Hagar and Hemmo (quant-ph/0512095)in which they suggest that information-theoretic approaches to quan-tum theory are incomplete.Quantum theory is a remarkably successful theory.There is little doubt as to what quantum theory says,at least in simple situations;predictions of quantum theory have been experimentally verified with great accuracy, and no prediction of quantum theory is known to be incorrect.On the other hand,there is no consensus as to what quantum theory means.In a recent article[1],Hagar and Hemmo(henceforth H2)have discussed the position,especially as set forth by Bub[2]and by Fuchs[3],that quan-tum theory should be considered to be about quantum information,rather than about quantum systems.H2suggest that the story of“Wigner’s friend”[4]would present a difficulty for this position,and in this note I wish to comment on this suggestion.To avert a possible misunderstanding,I should point out that H2also emphasize that the experimental successes of quan-tum theory do not rule out other theories which are,at least in principle, empirically distinguishable from quantum theory(they cite the model of Ghirardi,Rimini,and Weber[5]as an example),but that is not the aspect of their article upon which I will comment.For the purpose of this note,I will take quantum theory to be empirically completely correct.Here is a version of the story of Wigner’s friend,similar to the version told by H2:A friend of Wigner’s enters a room,which is then closed;Wigner remains outside.Inside the room is an electron,which has been prepared with its spin along the x-axis,so that|initial e=12[|↑ e+|↓ e].(1) Here subscript e refers to the electron,and|↑ e(|↓ e)represent states in which its spin is parallel(anti-parallel)to the z-axis.The room also contains a machine,whose operation I will describe below,but which is initially switched offand thus completely inert.After the room has been closed,Friend measures the component of spin of the electron along the z-axis.Wigner has been told that Friend would measure that spin component, but he does not know the result of the measurement,so Wigner assigns the following state-vector to the contents of the room:|Ψ =12[|↑ e|sees↑ R+|↓ e|sees↓ R],(2) where system R consists of the part of Friend which remembers the result of the measurement,together with anything else(other parts of Friend,the measuring apparatus,the air in the room...)with which that part may have become entangled.2I will discuss the two cases in which Friend does,or does not,switch on the machine after he has measured the spin.If he does not,then the machine remains inert,and so has no effect on the rest of our story.If the machine is switched on,here is what happens:there is a pointer mounted on the outside of the machine,which can point either to a mark“Y”or to a mark“N”;when switched on,the machine interacts with the combined system e⊗R with the result that if that system is described by the state-vector given in eq.2(as in fact it is)the pointer points to“Y”,but if the state-vector were orthogonal to that given in eq.2,it would point to “N”.Of course such a machine is completely impossible in practice[6],but having made the assumption that quantum theory gives correct answers in all circumstances,we are entitled to consider what would happen if such a machine were actually to exist.And what would happen is that,if Wigner enters the room after the machine has been switched on,he will surely see that the pointer indicates“Y”.In contrast to this,in a“collapse theory”such as that of[5],after the spin is measured by Friend,the state-vector of e⊗R quickly collapses to either thefirst or the second term on the right-hand side of eq.2,which would imply that the pointer would indicate“Y”only with probability1would indicate“Y”only with probability1first switched on the machine,and then made a second measurement of spin.Nevertheless he is predicting with certainty the results of two in-compatible measurements.Note that this conclusion does not depend on any identification of state-vectors as representing information,nor indeed on any commitment to what quantum theory means;statements A)and B)are just what quantum theory says.Statement B)is an elementary-textbook statement about a repeated measurement on a microscopic system, while statement A)requires us to trust what quantum theory says about (impossible-in-practice)measurements on macroscopic systems.Statements A)and B)together imply that Friend cannot ascribe any quantum state to the system e⊗R;there simply is no quantum state, neither pure nor mixed,which is compatible with statements A)and B)[8] The information which Friend has about the results of future measurements on the e⊗R system does not correspond to any quantum state of that system.Acknowledgement:I would like to acknowledge the hospitality of the Lawrence Berkeley National Laboratory,where this work was done. References[1]A.Hagar and M.Hemmo,“Explaining the Un observed—Why QuantumMechanics Ain’t Only About Information”,e-print quant-ph/0512095 (2005).[2]J.Bub,“Why the Quantum?”,Stud.Hist.Philos.Modern Phys.35B,241(2004);“Quantum Mechanics is About Quantum Information”, Found.Phys.35,541(2005).[3]C.A.Fuchs,“Quantum Mechanics as Quantum Information(and onlya little more)”,e-print quant-ph/0205039(2002).[4]E.P.Wigner,“Remarks on the Mind-Body Question”,in The Scien-tist Speculates,I.J.Good,ed.,William Heinemann,London(1961), reprinted in Symmetries and Reflections,Indiana University Press, Bloomington(1967).[5]G.C.Ghirardi,A.Rimini,and T.Weber,“Unified dynamics for micro-scopic and macroscopic systems”,Phys.Rev.D34,470(1986).5[6]It would also be impossible in principle,unless the machine were allowedto interact with anything with which Friend might be entangled,which is why I chose to define the system R in the way I did.A more-usual treatment would be to not mention this issue under the(almost-surely correct)assumption that the reader already understands it.[7]We could even go further and state that Friend therefore knows that ifhe himself should look at the pointer after turning on the machine,he would see it indicating“Y”.[8]For a simple proof of this,let PΨbe the projector|Ψ Ψ|(where|Ψ is given in eq.2),let P↑be the projector(|↑ e ↑|)⊗I R,and suppose there were a density operatorρfor the e⊗R system.Then statementA)would requireProbability(“Y”)=Tr(PΨρ)=1,(4) while statement B)would requireProbability(“↑”)=Tr(P↑ρ)=1.(5) Eq.4has the unique solutionρ=|Ψ Ψ|(again,|Ψ from eq.2),but with that solution forρ,eq.5reads1。