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arXiv:quant-ph/0210060

A single quantum cannot be teleported

Daniele Tommasini

Published Oct 9, 2002• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0210060

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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.
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 teleportation is one of the most enigmatic protocols realized so far in the area of quantum information, allowing for the transfer of quantum information assisted by an entangled state. It was a subject of science fiction 20 years ago, but now is a fundamental experimental protocol and quantum primitive for quantum information processing tasks. There have been many successful realizations of teleportation ranging from those using photons, atoms, and hybrid systems and long-range teleportation beyond 100km has already been achieved multiple times. These however typically involve explicitly single particle systems or effective few-particle systems. For larger (visible to the naked eye) objects involving many particles, teleportation is typically more difficult due to the fast decoherence such macroscopic objects suffer. In this case, the entanglement disappears almost as soon as it is created, making it useless for such tasks. More recently, teleportation was accomplished in the continuous variables (CV) framework between two atomic ensembles [1]. As remarkable as these achievements are, teleportation schemes that are known today (qubit/CV) do not allow us to teleport more complex quantum states at the macroscopic level. For example, while it is possible in principle to extend teleportation to multiple qubits, on a macroscopic level this is prohibitively complicated and highly susceptible to decoherence. For atomic ensemble CV based schemes, the teleported states are restricted to small displacements from the completely Sx-polarized state on the Bloch sphere.
In port-based teleportation, Alice teleports an unknown quantum state $|\ensuremath{\psi}\ensuremath{\rangle}$ to one of NNN ports at Bob's site. Alice applies a measurement and sends Bob the outcome kkk. Bob only needs to select the kkkth port in order to obtain $|\ensuremath{\psi}\ensuremath{\rangle}$. We present a theorem in the spirit of the no-cloning theorem, which says that it is impossible to extract any information from an unknown quantum state if only a single copy of it is provided and if the state remains unchanged. We use this theorem and the no-signaling principle to prove an upper bound on the success probability of port-based teleportation.
By quantum teleportation an unknown quantum state is destroyed at a sending place while its perfect replica state appears at a remote place via dual quantum and classical channels. Quantum teleportation allows for the transmission of quantum information to a distant location despite the impossibility of measuring or broadcasting the information to be transmitted. e classical teleportation is like a fax in which one could scan an object and send the information so that the object can be reconstructed at the destination. In this conventional facsimile transmission, the original object is scanned to extract partial information about it. e scanned information is then sent to the receiving station, where it is used to produce an approximate copy of the original object. e original object remains intact a er the scanning process. By contrast, in quantum teleportation, the uncertainty principle forbids any scanning process from extracting all the information in a quantum state. e nonlocal property of quantum mechanics enables the striking phenomenon of quantum teleportation. Bennett and coworkers28 showed that a quantum state can be teleported, provided one does not know that state, using a celebrated and paradoxical feature of quantum mechanics known as the Einstein-Podolsky-Rosen (EPR) e ect.11 ey found a way to scan out part of the information from an object A, which one wishes to teleport, while causing the remaining part of the information to pass to an object B, via the EPR e ect. In this process, two objects B and C form an entangled pair; object C is taken to the sending station, while object B is taken to the receiving station. At the sending station, object C is scanned together with the original object A, yielding some information and totally disrupting the state of A and C. e scanned information is sent to the receiving station, where it is used to select one of several treatments to be applied to object B, thereby putting B into an exact replica of the former state of A.
Quantum teleportation, a cornerstone of quantum information science, allows for the transfer of an unknown quantum state without physically moving the associated quantum particle. This process critically relies on shared entanglement and classical communication. A fundamental aspect of quantum information is the no-cloning theorem, which dictates that an arbitrary unknown quantum state cannot be perfectly copied. This paper investigates the intrinsic connection between Bell nonlocality, a profound manifestation of quantum entanglement, and the inherent unclonability of quantum teleportation. We argue that the very existence of Bell nonlocality within the shared entangled resource not only enables quantum teleportation but also fundamentally guarantees that the teleported state cannot be perfectly cloned. By examining the theoretical underpinnings of Bell's theorem and the quantum teleportation protocol, we demonstrate how the non-local correlations preclude any possibility of state duplication, thereby upholding the no-cloning theorem. This connection is vital for understanding the security and foundational aspects of quantum communication, establishing Bell nonlocality as a strong certification of secure, non-duplicable quantum state transfer. The analysis highlights that successful quantum teleportation, intrinsically linked to the violation of Bell inequalities, provides an experimental signature of the non-classical correlations that underpin security against cloning.