The Structure and Quantum Capacity of a Partially Degradable Quantum Channel

Abstract

The quantum capacity of degradable quantum channels has been proven to be additive. On the other hand, there is no general rule for the behavior of quantum capacity for antidegradable quantum channels. We introduce the set of partially degradable (PD) quantum channels to answer the question of additivity of quantum capacity for a well-separable subset of antidegradable channels. A quantum channel is PD if the channel output can be used to simulate the degraded environment state. The PD channels could exist both in the degradable, antidegradable and conjugate degradable family. We define the term partial simulation, which is a clear benefit that arises from the structure of the complementary channel of a PD channel. We prove that the quantum capacity of an arbitrary dimensional PD channel is additive. We also demonstrate that better quantum data rates can be achieved over a PD channel in comparison with standard (non-PD) channels. Our results indicate that the partial degradability property can be exploited and yet still hold many benefits for quantum communications.INDEX TERMS Quantum channels, quantum capacity, degradability, partially degradable channels, partial simulations, quantum Shannon theory.

The private classical capacity of a partially degradable quantum channel

“…Second, the PD channel structure allows similar benefits in the world of antidegradable channels to the Hadamard channels in the degradable set, since the evaluation of its quantum capacity can easily be made in arbitrary dimensions. Similar to degradable channels [5], [9], the quantum capacity of a PD channel has been proven to be additive [1]. However, no similar results were obtained for the private classical capacity.…”

“…The existence of partially degradable (PD) channels has been recently investigated, and it was shown that PD channels exist in the world of those qudit channels that have entanglementbinding complementary channels [1]. The PD channel set involves conjugate-PD channels, which represent a subset in the conjugate degradable channels; this set was introduced by Bradler et al [11].…”

“…The sets of more capable and less noisy quantum channels were defined by Watanabe [2], and it was further demonstrated that other, well-characterized channel sets could be defined beyond the degradable and conjugate-degradable channels. The quantum capacity [3], [6][7][8], [12][13][14][15][16] of some of these channels also single-letterizes, similar to the quantum capacity of PD channels [1]. However, at this point, the exact connection between these channel sets and PD channels is still open.…”

“…It is clear, that a PD channel is equipped with the benefits of both the more capable and less noisy sets. However, in contrary to the more capable and less noisy sets, a PD channel can be also an anti-degradable one, since the structure of the complementary channels (the channel between the sender and the environment) differs at several points [1]. On the other hand, despite the lack of exact clarification of the connections between the sets, some properties of these channels can be exploited and combined together with the structural properties of PD channels to derive further valuable results regarding the capabilities of a PD channel.…”

A statistical model of information evaporation of perfectly reflecting black holes

“…The process of quantum information transmission through a perfectly reflecting (PR) black hole (BH) can be evaluated via a noisy quantum channel that clones the absorbed quantum system and evaporates the cloned particles [1]. The application of quantum Shannon theory [14] in black hole physics [2][3][4][5][6][7][8][9][10], [19], [21][22][23][24][25][26][27][28][29][30], reduced the description of the evaporation process into the use of the tools of this field and made the situation well tractable. The black hole evaporation is still actively studied, particularly the appropriate statistical model for the internal evolution processes is still missing.…”