The private classical capacity and quantum capacity of a quantum channel

By Igor Devetak. IEEE Transactions on Information Theory, 2003

773 citations recorded by the source corpus.

A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/32d855b63adf9f704ac01d2652b3ac26b4bab553

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, background): “In contrast to the classical case, a quantum channel has various distinct capacities [2–7].”
Quantum entanglement (2007, positive): “This was also used by Devetak to provide the first fully rigorous proof of quantum Shannon theorem, saying that capacity of quantum channel is given by coherent information (Devetak, 2003).”
Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “[52] I.”
Advances in quantum cryptography (2019, neutral): “, the maximum rate at which Alice may deterministically transmit secret bits [581].”
The mother of all protocols: restructuring quantum information’s family tree (2006, background): “1999, 2002), the quantum capacity of a quantum channel (Lloyd 1996; Shor 2002; Devetak 2005) and the best ways to use noisy entanglement to extract pure entanglement (Devetak & Winter 2005) or to help send classical information (Horodecki et al.”
Entanglement of assistance and multipartite state distillation (2005, methodology): “…to theorem 1. can i | i Then we deﬁne a new quantum channel which, by theorem 1, has on the test state | φ ⊗ n the coherent information [30] (cid:8) (cid:0) (cid:1)(cid:9) Invoking the quantum channel coding theorem [8, 25, 31], there are block codes for T ′ achieving this rate asymptotically.”
Fundamental limits of repeaterless quantum communications (2015, neutral): “bound of Eq. (S257) is tight for dephasing and erasure channels. The next non-trivial generalization is moving from quantum to private communication. In this regard, the notions of private capacities [S71] and private states [S11, S12] were available well after 1996. Note that we may consider the se”
Quantum channels and memory effects (2012, methodology): “Following (Devetak, 2005) a relatively simple proof of the direct part of the theorem instead can be obtained as a modification of the coding theorem for the private classical capacity.”
Quantum Computation and Information (2006, methodology): “A few years later, the Holevo-Schumacher-Westmoreland Theorem [66, 46] gave us the capacity of a noisy quantum channel for classical information and the fully quantum analog of Shannon’s Noisy Channel Coding Theorem [68] was finally obtained in 2005, by Igor Devetak [33].”
The structure of degradable quantum channels (2008, background): “Furthermore, Yard, Devetak, and Hayden have shown [41] that the coherent information of a degradable channel is concave as a function of reference state, so that the required optimization can be performed eﬃciently and the capacity problem for such channels has been completely resolved.”
Aspects of Generic Entanglement (2004, background): “One can also quantify the amount of secret key K(σ) distillable against an eavesdropper holding the purification of the state (see [ 8 , 10, 11] and references therein), and the distillable “common randomness” CR(σ ) [2, 9] (discounting at the end of the protocol the amount of communication used).”
A Survey on Quantum Channel Capacities (2018, background): “In the case of a classical channel, we can send only classical information while quantum channels extend the possibilities, and besides the classical information we can deliver entanglement-assisted classical information, private classical information, and of course, quantum information [54], [136].”