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

Abstract

Complications in preparing and preserving quantum correlations stimulate recycling of a single quantum resource in information processing and communication tasks multiple times. 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 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.

Creating quantum correlations in generalized entanglement swapping

“…It can be observed that each of the above three states is entangled for the whole range of λ except at λ = 0. This result demonstrates the following interesting aspect of the generalized entanglement swapping protocol with the POVM (24). This protocol creates entanglement in the pair (1,4).…”

“…Therefore, the above results indicate that the resulting state ρ 14|i (for all possible outcomes i) after completion of our generalized entanglement swapping protocol contingent upon using the POVM (24) with x = 0.3 is entangled, but does not violate the three-setting steering inequality [51] or the Bell-CHSH inequality. This is summarized in Table II.…”

“…Variation of negativity (E ρ , E ρ 12|i , and E ρ 34|i ) with the measurement parameter λ for the states ρ 12|i , ρ 34|i , and ρ 14|i . Here ρ αβ|i denotes the postmeasurement state for the pair (α, β) after Bob gets the outcome i (i ∈ {1, 2, 3, 4}) contingent upon performing the POVM (24) with x = 0.3 and communicates the outcome to Alice and Charlie. This plot is the same for all possible outcomes i ∈ {1, 2, 3, 4} of Bob's measurement.…”

“…Now, we consider the POVM mentioned in (24) with x = 0.725. For this POVM, we will now determine how different quantum correlations are created or destroyed in various pairs of particles.…”

“…A general quantum measurement is represented by a positive operator-valued measure (POVM) [11,12]. POVMs have been shown to possess operational advantages in many tasks over projective measurements, for example, in the context of distinguishing nonorthogonal quantum states [13], demonstrating hidden nonlocality [14,15], probing temporal correlations [16], sequential detection of quantum correlations by multiple observers [17][18][19][20][21], recycling resources in information theoretic tasks [22][23][24][25], 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.…”