Quantum entanglement through hidden dimensions

Guillaume Aubrun

Vlatko Vedral

I exploit the formal equivalence between the ground state of a d-dimensional quantum system and a d + 1-dimensional classical Ising chain to represent quantum entanglement in terms of classical correlations only. This offers a general “local hidden variable model” for all quantum phenomena existing in one dimension lower than the (hidden variable) classical model itself. The local hidden variable model is not contradicted by the implications of Bell's theorem. Formal theory is presented first and then exemplified by the quantum Ising spin chain in a transverse magnetic field. Here I explicitly show how to derive any two site entanglement in the transverse model from the partition function of the classical Ising spin chain existing in two dimensions. Some speculations are then presented regarding possible fundamental implications of these results.

Shengjun Wu

Mao-Sheng Li, Zhu‐Jun Zheng

Abstract Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder (2021 Phys. Rev. A 104 L050201) studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. The set with such property is called to have hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. Unexpectedly, the constructions of genuine hidden nonlocal sets without entanglement seems to be easier than that with entanglement. Therefore, from this perspective, this kind of nonlocality is rather different from the Bell nonlocality.

ARTUR K. EKERT

Jyun-Yi Li, Xiao‐Xu Fang, Ting Zhang +3 more

Ideal quantum teleportation transfers an unknown quantum state intact from one party Alice to the other Bob via the use of a maximally entangled state and the communication of classical information.If Alice and Bob do not share entanglement, the maximal average fidelity between the state to be teleported and the state received, according to a classical measure-and-prepare scheme, is upper bounded by a function f c that is inversely proportional to the Hilbert space dimension.In fact, even if they share entanglement, the so-called teleportation fidelity may still be less than the classical threshold f c .For two-qubit entangled states, conditioned on a successful local filtering, the teleportation fidelity can always be activated, i.e., boosted beyond f c .Here, for all dimensions larger than two, we show that the teleportation power hidden in a subset of entangled two-qudit Werner states can also be activated.In addition, we show that an entire family of two-qudit rank-deficient states violates the reduction criterion of separability, and thus their teleportation power is either above the classical threshold or can be activated.Using hybrid entanglement prepared in photon pairs, we also provide the first proof-of-principle experimental demonstration of the activation of teleportation power hidden in this latter family of qubit states.The connection between the possibility of activating hidden teleportation power with the closely-related problem of entanglement distillation is discussed.