Ability of unbounded pairs of observers to achieve quantum advantage in random access codes with a single pair of qubits

Abstract

Recycling a single quantum resource in information processing and communication tasks multiple times is of paramount significance from foundational and practical perspective. Here we consider a scenario involving multiple independent pairs of observers acting with unbiased inputs on a single pair of spatially separated qubits sequentially. In this scenario, we address whether more than one pair of observers can demonstrate quantum advantage in some specific 2 → 1 and 3 → 1 random access codes. Interestingly, we not only address these in the affirmative, but also illustrate that an unbounded pairs can exhibit quantum advantage. Furthermore, these results remain valid even when all observers perform suitable projective measurements and an appropriate separable state is initially shared.

Limitations on sharing Bell nonlocality between sequential pairs of observers

“…(S.21)-(S.23) above, it follows for unbiased observables that the CHSH parameters for each pair (A j , B k ) are convexlinear in the spin correlation matrix T of the initial state (and are independent of the Bloch vectors). Further, any physical spin correlation matrix T can be written as a convex combination of the spin correlation matrices of maximally entangled states, as follows from the proof of Proposition 1 of [36] (in particular, T can be expressed as a mixture of the four Bell states corresponding to a basis in which T is diagonal). Now, any maximally entangled spin correlation matrix can be written as T me = R T 0 R , where T 0 = −I is the spin correlation matrix of the singlet state and R , R are local rotations of the first and second qubits.…”

“…We propose testing the latter experimentally, as it in principle permits four independent pairs of observers to generate Bell nonlocality, and hence to carry out device independent quantum information protocols such as randomness generation, via the recycling of a two-qubit state. Further details and generalisations of our methods are given in [26], and we expect these methods can also be readily applied to the sequential sharing of quantum properties such as entanglement [32], Einstein-Podolsky-Rosen steering [33], and random access codes [34][35][36].…”

Resource theoretic efficacy of the single copy of a two-qubit entangled state in a sequential network

“…A fertile direction of study could also be to generalize the scheme formulated in the present paper towards studying resource theoretic efficacy of sequential sharing of single-shot entanglement in the context of multi-qubit and two-qudit higher dimensional entangled states. Finally, categorizing various information processing tasks involving sequential measurements [49][50][51][52][53][54][55][56]59] in terms of their resource theoretic advantages is another potentially attractive direction of future study.…”

“…Applications of sequential detection of quantum correlations in different information processing tasks have also been reported [49][50][51][52][53][54][55][56]. Recently, the technique of choosing different sharpness parameters for the different measurement settings of each observer has been proposed for obtaining the possibility of unbounded number of observers sharing Bell-nonlocality [43,57,58], and this type of result has also been probed towards random access code generation [59].…”

Creating quantum correlations in generalized entanglement swapping

“…A general quantum measurement is represented by a positive operatorvalued measure (POVM) [10,11]. POVM has been shown to possess operational advantages in many tasks over projective measurements, for example, in the context of distinguishing non-orthogonal quantum states [12], demonstrating hid-den nonlocality [13,14], probing temporal correlations [15], sequential detection of quantum correlations by multiple observers [16][17][18][19][20], recycling resources in information theoretic tasks [21][22][23] and so on. Here, our aim is to investigate how different types of quantum correlations are generated in the pair (1,4) and are deteriorated in the pairs (1,2) and (3,4) depending on the choice of the POVM by Bob.…”