Quantum entanglement from random measurements

Abstract

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 were available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarisers 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 emphasise how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilised randomness and should find practical applications in experimental confirmation of multi-photon entanglement or space experiments.PACS numbers: 03.65.UdQuantum mechanics imposes no limits on the spatial separation between entangled particles. This naturally leads one to ask whether observers that have never met and do not share a common reference frame can still detect effects of quantum entanglement. One can further ask if in every experimental run each observer's local reference frame needs to be composed of a huge number of somewhat correlated elementary systems (as it is the case for Stern-Gerlach magnets, polarisers, etc.), or if the effects of entanglement can be detected with references composed of only a few systems.Individually both of these questions have been addressed before. It is known that entanglement can be detected, cryptography can be realised, and Bell inequalities can be violated without a shared reference frame [1][2][3][4][5][6][7][8][9][10][11][12][13] and non-classical correlations can also be observed with finite-size references which are to some degree correlated [14][15][16]. Here we simultaneously address both questions and show that observers who have independent reference frames in an unknown state can each use a single spin-1 2 of the reference per experimental run in order to detect entanglement. If the state of the reference can be controlled a single spin-1 2 of it per experimental run will be shown to be sufficient to observe all phenomena that one can observe with macroscopic references in every experimental run.These findings have both practical and fundamental aspects. On the practical side, they show that entanglement detection is possible with independent reference frames and hence observers can save on communication resources [17][18][19][20] or pre-established quantum entanglement [21,22] that would have to be consumed to correlate local reference frames. On the fundamental side, bounded reference frames were discussed in the context of quantum-to-classical transition [14], where it was noted that the lack of perfect reference frames leads to "intrinsic ...

Genuine N -partite entanglement without N -partite correlation functions

“…It turns out that for pure states the existence of entanglement is fully captured by N -partite correlation functions only: A pure state is entangled if and only if the sum of squared N -partite correlation functions exceeds certain bound [3][4][5][6][7]. One may then wonder if similar detection methods could exist for mixed states, i.e.…”

“…Our aim is to verify to a high precision whether an anti-state exists to a preselected state |ψ . In our numerical approach we parameterize a candidate state |φ and use Simulated Annealing [17] to globally minimize the length of correlation [6] of the even mixture ρ = …”

Correlations between outcomes of random measurements

“…To estimate R, it would seem that we have to take into account all local directions but in fact it is sufficient to consider only a set of orthogonal axes for each party [1]:…”

“…It has been shown in Refs. [1,[4][5][6] that C > 1 if and only if the system is in a pure entangled state. In Appendix A we present a simple alternative proof for pure systems of two and three qubits that follows directly from the Schmidt decomposition.…”

“…One might therefore ask if correlations between randomly chosen observables reveal entanglement. We have recently shown that such "random correlations" are indeed the feature of entangled pure states [1]: A pure N -particle state is entangled if and only if the squared N -partite correlation functions averaged over uniform choices of local observables exceed certain bound.…”