Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Abstract

Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the entanglement-assisted classical capacity for any channel is additive, making entanglement across channel uses unnecessary. If the entanglement assistance is limited, the picture is much more unclear. Suppose the classical capacity is superadditive, then the classical capacity with limited entanglement assistance could retain superadditivity by continuity arguments. If the classical capacity is additive, it is unknown if superadditivity can still be developed with limited entanglement assistance. We show this is possible, by providing an example. We construct a channel for which the classical capacity is additive, but that with limited entanglement assistance can be superadditive. This shows entanglement plays a weird role in communication, and we still understand very little about it. DOI: 10.1103/PhysRevLett.119.040503 In Shannon's classical information theory [1], a classical (memoryless) channel is a probabilistic map from input states to output states. This has been extended to the quantum world. A (memoryless) quantum channel is a time-invariant completely positive trace preserving (CPTP) linear map from input quantum states to output quantum states [2]. A classical channel can only transmit classical information, and the maximum communication rate is fully characterized by its capacity. A quantum channel can be used to transmit not only classical information but also quantum information. Hence, there are different types of capacity, such as classical capacity C for classical communication [3,4] and quantum capacity Q for quantum communication [5][6][7].Since quantum channels transmit quantum states, and quantum states can be entangled with other parties, it is natural to ask if entanglement can assist the communication. This was first considered by Bennett et al., who showed that unlimited preshared entanglement could improve the classical capacity of a noisy channel [8,9]. Shor examined the case where only finite preshared entanglement is available and obtained a trade-off curve that illustrates how the optimal rate of classical communication depends on the amount of entanglement assistance (CE trade-off) [10]. One can also consider how entanglement (E), classical communication (C), or quantum communication (Q) can trade-off against each other as resources. The trade-off capacity of almost any two resources was studied by Devetak et al. [11,12], such as entanglement-assisted quantum capacity (QE trade-off). Subsequently, the triple resource (CQE) trade-off capacity was also characterized [13][14][15].However, almost all the capacity formulas above are given by regularized expressions. They are difficult to evaluate because they require an optimization over an infinite number of channel uses, which is typically intractable. The existence of this regularization is because entanglement acr...

Practical Route to Entanglement-Assisted Communication Over Noisy Bosonic Channels

“…where A ± = (D − 1 ± (N S − N S ))/2, N S = κN S + N B and D = (N S + N S + 1) 2 − 4κN S (N S + 1). Various aspects of EA communication have been explored, including extensions to limited pure entanglement [44], noisy entanglement [45], trade-off capacities [35,46], and superaddivity issues [47,48].…”

μSR study of the triangular Ising antiferromagnet ErMgGaO4

“…Such frustration frequently arises from antiferromagnetically coupled spins located on triangle-based lattices (stacked triangular, kagome, pyrochlore), and can lead to a highly degenerate ground state without magnetic order. The previously studied quasi-two dimensional triangular layered material YbMgGaO 4 (with YbFe 2 O 4 -type structure) has been attracting considerable interest as a potential quantum spin liquid candidate [6][7][8][9][10][11][12].YbMgGaO 4 has a Curie-Weiss temperature of ∼ -4 K but shows no sign of long-range order down to 30 mK [6,7,9,10]. Its magnetic specific heat in zero field shows a broad hump at 2.4 K instead of sharp λ-type peak which would be expected for a well-defined second order phase transition.…”

“…Such frustration frequently arises from antiferromagnetically coupled spins located on triangle-based lattices (stacked triangular, kagome, pyrochlore), and can lead to a highly degenerate ground state without magnetic order. The previously studied quasi-two dimensional triangular layered material YbMgGaO 4 (with YbFe 2 O 4 -type structure) has been attracting considerable interest as a potential quantum spin liquid candidate [6][7][8][9][10][11][12].…”

“…The magnetic excitation spectra appears as a broad continuum in inelastic neutron scattering measurements, which has been taken as an evidence for a QSL state [7,10]. Particularly, the anisotropic exchange interactions between rare earth ions are found to be playing a crucial role in stabilizing such spin liquid ground state [6][7][8][9][10], although an alternative explanantion in terms of the random Ga/Mg site mixing has also been proposed [11]. Such exchange interactions associated with spin orbit coupling strongly depends on rare earth ions.…”

Precursors to Exciton Condensation in Quantum Hall Bilayers

“…At some critical layer separation d c a transition to the incompressible exciton condensate occurs. The nature of this transition, and of the bilayer 2DES generally at d d c , remain poorly understood despite intensive and ongoing study [14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”