Im struggling to understand the no cloning theorem and its consequences. The no cloning theorem states according to wikipedia. For the love of physics walter lewin may 16, 2011 duration. For example, we considered the following problem in homework 1. The no cloning theorem prevents us from using classical error correction techniques on quantum states. The no cloning theorem is therefore a substantial restriction on the facilities available to the programmer of a quantum computer. The no cloning theorem but in the quantum world, the laws of physics impose a severe restriction on copying. Nocloning theorem proof nobroadcast theorem quantum. Fortunately for alice and bob, it is possible to place strict theoretical limits the nocloning theorem william k. The no cloning theorem says that the equivalent for a quantum computer is not possible even in principle. It says that it is not possible to combine basic structural features of quantum entanglement with a uniform cloning operation without collapsing to degeneracy.
It is impossible to make a perfect copy of an unknown state. In physics, the nocloning theorem states that it is impossible to create an identical copy of an. However, the initial state vector prior to cloning given by eq. The cloning collapse theorem can be read as a no go theorem.
As such, we proceed with the initial state given by eq. Note that in this example one could interpret the oscilla. The claim of the nocloning theorem is that in the case of quantum information perfect copying is impossible. In the following, we first prove that, as a strict principle, the nocloning theorem prohibits any perfect cloning of quantum states, no matter the orthogonal oorthogonal. Thought experiment about nocloning theorem and ftl information. Again, these results rely on the noncartesian tensor product in hilb. The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. The nocloning theorem our nexttolast key concept is the nocloning theorem. The last part of the lecture is devoted to the epr experiment and bells inequality. The nocloning theorem cloning has been in the news a lot lately.
The no cloning theorem extends to all dagger compact categories. If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. We also describe in detail the protocol of quantum teleportation and give an example of its physical implementation. Nocloning theorem distinctive features of quantum computations. In this paper, we will prove that, due to the uncontrollable quantum fluctuations, no perfect cloning can be achieved. The quantum mechanical no cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product construction or finite dimension as required in other generalizations. As far as i am aware the theorem is usually proofen by contradiction, i. We analyze to what extent it is possible to copy arbitrary states of a twolevel quantum system. A general nocloning theorem for an infinite multiverse. The no cloning theorem our nexttolast key concept is the no cloning theorem. In quantum physics the nocloning theorem is the statement that one cannot produce a second copy of an arbitrary given quantum state by a quantum physical process more in detail, in its original version the statement is that given a quantum system with hilbert space h h and with a chosen initial pure quantum state e. Apr 19, 2019 however, the initial state vector prior to cloning given by eq. The difficulty stems from the inherent nonlinearity of copying. Seen the elementary nature of its proof, the nocloning theorem and its gener.
A brief introduction to no cloning theorem, teleportation and povm. For example, you might make a copy of a le containing your latextyped homework to keep. Indeed, optimal approximate cloning is, in principle, one of the best methods eve can use against quantum cryptography. Jun 28, 2016 thus, the no cloning of quantum steering verified by equation 2 shows that ruling out false steering secures channels against cloning based attacks when implementing quantum key distribution. Experimental quantum cloning in a pseudounitary system xiang zhan, kunkun wang. Pdf no cloning theorem with essential mathematics and. This no go theorem of quantum mechanics was articulated by james park in proving the impossibility of a simple perfect nondisturbing measurement scheme, in 1970 and rediscovered by wootters and zurek and by dieks in 1982.
The quantum no cloning theorem states that one cannot build a perfect cloning device for arbitrary quantum systems there also exists a famous thought experiment where alice transmits information to bob superluminously using a quantum cloning device, which is resolved by the no clone theorem. In particular, in the presence of linear and quadratic terms of momentum in generalized uncertainty principle, we rst compute the energy density at a given modi ed temperature and then using the modi ed stefanboltzmann law we derive the modi ed page time. The argument for the no cloning theorem in qm goes back to the papers of wootters and zurek and dieks. Nocloning theorem ebooks read ebooks online free ebooks. For example, we considered the following problem in homework 2. H e \in h, then there is no unitary operator on the tensor product. Nonclassical conditional probability and the quantum no. No cloning theorem and deutschjozsa algorithm are introduced. Simply put, if you are holding a qubit that is in an unknown state, it is impossible to make a perfect, independent unentangled copy of the qubit in all cases.
It also implies the standard restrictions on measuring noncommuting observables. Adams discusses the basic principles of quantum computing. Ccsphys c191 no cloning, teleportation 91505 lecture 6. Implications of the noclone theorem physics forums. A simple theorem is proved which has most of the known no cloning and no broadcasting results as corollaries. The figure illustrates the general argument with a specific example. The no cloning theorem is not just a negative resultin fact, it is the starting point for the miracle of quantum cryptography, which offers a new level of security, guaranteed by the laws of nature itself. However, the no cloning theorem is even more important in quantum cryptography, where the. The theorem partial cloning summary prerequisites the result pt. The discovery of this important theorem for the field of quantum information is currently dated 1982. V agenas 1, a, ahmed farag ali 2, 3, b, hassan alshal 4, 5, c 1 theoretical physics group, department of physics, kuwait university, p. T wo proofs of the nocloning theorem 1,2 have been published in 1982, both triggered by a claim that the use of entangled states would allow one to transmit information with superluminal speed. Bill wootters is a professor of physics at williams college in williamstown, massachusetts. It says that if we construct a cloning operator u it will be able to just copy orthogonal states, but i dont fully grasp what is meant by that, both abstractly and practically.
This statement, known as the nocloning theorem, prohibits perfect cloning, but doesnt oppose approximate copying. Below we prove that universal perfect classical cloning machines violate the liouvilledynamics governing the evolution of statistical ensembles. Ccsphys c191 no cloning, teleportation 91505 lecture 6 1. Classical nocloning theorem connecting repositories. No cloning theorem and teleportation 1 no cloning theorem a quantum operation which copied states would be very useful. The nocloning theorem understanding quantum computers. Secondly, we illustrate that, leibnizs principle r non has an equivalent meaning to the nocloning theorem, which thus can be stated by a unified scheme that any. The impossibility of cloning an unknown quantum state is one of the basic rules governing quantum physics. In physics, the no cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. Nocloning theorem, leibnizs principle, and the notion of. A classical version of the nocloning theorem is discussed. But today we are not going to talk about that type of cloning, but instead of a process of duplicating. We begin in this lecture with cloning, quantum entanglement, and density operators.
After that, drunk or not, i would have staggered home in dizzy high spirits. In particular, the nocloning theorem is proved, which forbids one to copy a qubit. This theorem essentially states that nonorthogonal states of a closed quantum system cannot be reliably distinguished, and hence cannot be copied. In this report, i present the idea of no cloning theorem, which was proposed by wootters and zurek. Nocloning of quantum steering npj quantum information. Wootters and zurek even question the very notion of quantum state in.
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