Quantum Entanglement Capacity with Classical Feedback

For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback ($E_B$), and we show that this quantity lies between two other well-studied quantities. These two quantities - namely the quantum capacity assisted by two-way classical communication ($Q_2$) and the quantum capacity with classical feedback ($Q_B$) - are widely conjectured to be different: there exists quantum discrete memoryless channel for which $Q_2>Q_B$. We then present a general scheme to convert any quantum error-correcting codes into adaptive protocols for this newly-defined quantity of the quantum depolarizing channel, and illustrate with Cat (repetition) code and Shor code. We contrast the present notion with entanglement purification protocols by showing that whilst the Leung-Shor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned Cat code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any $E_B$ protocols. We then apply this formula to the $E_B$ protocols that we discuss to obtain new lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel

Comparisons of soil suction induced by evapotranspiration and transpiration of S. <i>heptaphylla</i>

For a given evapotranspiration (ETr), both soil evaporation and plant transpiration (Tr) would induce soil suction. However, the relative contribution of these two processes to the amount of suction induced is not clear. The objective of this study is to quantify ETr- and Tr-induced suction by a selected tree species, Scheffllera heptaphylla, in silty sand. The relative contribution of transpiration and evaporation to the responses of suction is then explored based on observed differences in Tr- and ETr-induced suction. In total, 12 test boxes were used for testing: 10 for vegetated soil with different values of leaf area index (LAI) and root area index (RAI), while two were for bare soil as references. Each box was exposed to identical atmospheric conditions controlled in a plant room for monitoring suction responses over a week. Due to the additional effects of soil evaporation, ETr-induced suction could be 3%–47% higher than Tr-induced suction, depending on LAI. The significance of evaporation reduced substantially when LAI was higher, as relatively less radiant energy fell on the soil surface for evaporation. For a given LAI, the effects of evaporation were less significant at deeper depths within the root zone. The effects of RAI associated with root-water uptake upon transpiration were the dominant process of ETr affecting the suction responses.</jats:p

Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet

We argue that the S=1/2 kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For $D<D_c$ the system is in a moment-free phase and for $D>D_c$ the system develops antiferromagnetic long-range order. The quantum critical point is found to be $D_c \simeq 0.1J$ using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu$_3(OH)$_6$Cl$_3$ may be in a quantum critical region controlled by this fixed point.Comment: 5 pages, 4 figures; v2: add. data included, show that D=0.1J is at a quantum critical poin

On the capacities of bipartite Hamiltonians and unitary gates

We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted one-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.Comment: V3: extensively rewritten. V4: a mistaken reference to a conjecture by Kraus and Cirac [quant-ph/0011050] removed and a mistake in the order of authors in Ref. [53] correcte

Oblivious remote state preparation

We consider remote state preparation protocols for a set of pure states whose projectors form a basis for operators acting on the input Hilbert space. If a protocol (1) uses only forward communication and entanglement, (2) deterministically prepares an exact copy of the state, and (3) does so obliviously -- without leaking further information about the state to the receiver -- then the protocol can be modified to require from the sender only a single specimen of the state. Furthermore, the original protocol and the modified protocol use the same amount of classical communication. Thus, under the three conditions stated, remote state preparation requires at least as much classical communication as teleportation, as Lo has conjectured [PRA 62 (2000) 012313], which is twice the expected classical communication cost of some existing nonoblivious protocols