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arXiv:2303.17549 · Physical Review A

Witnessing entanglement of remote particles with incomplete teleportation

Vahid Jannesary, Fatemeh Rezazadeh, Sadegh Raeisi, Vahid Karimipour

Published Oct 23, 2023• 1 citation
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Abstract

Having common reference frames or aligned coordinate systems is one of the presumptions in witnessing entanglement in a two-party state possessed by two remote parties. This assumption may fail for many reasons. With an unlimited supply of singlet states, the two parties can first align their coordinate systems and then measure any entanglement witness. In this paper, we propose an alternative method which uses the same resource for incomplete teleportation of states between the two parties, enabling them to witness the entanglement of any shared state by local measurements without the need for prior alignment of the coordinate systems. The method works for any kind of witness and in any dimension. Beyond the context of entanglement witnesses, our method works also for remote measurements of observables of particles (entangled or not) in laboratories which may have deficiency in their resources.

DOI
10.1103/physreva.108.042421

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We present a scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other proposals, our scheme requires the same amount of classical communication and entangled resources as conventional teleportation, does not reveal any reference frame information, and is robust against changes in reference frame alignment while the protocol is under way. The mathematical foundation of our scheme is a unitary error basis which is permuted up to a phase by the conjugation action of the group. We completely classify such unitary error bases for qubits, exhibit constructions in higher dimension, and provide a method for proving nonexistence in some cases.
We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states, which can be directly experimentally assessed if two copies of the state are available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarizers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run, access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and, in fact, observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasize how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilized randomness and should find practical applications in experimental confirmation of multiphoton entanglement or space experiments.
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Single-photon entangled states, i.e., states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped, and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one to say whether a given state is path entangled and also that entanglement lies in the subspace, where the optical paths are each filled with one photon at most, i.e., refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system. Our work provides a simple and trustworthy method for verifying the proper functioning of future quantum networks.
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