Fundamental Limits on the Capacities of Bipartite Quantum Interactions

Abstract

Bipartite quantum interactions have applications in a number of different areas of quantum physics, reaching from fundamental areas such as quantum thermodynamics and the theory of quantum measurements to other applications such as quantum computers, quantum key distribution, and other information processing protocols. A particular aspect of the study of bipartite interactions is concerned with the entanglement that can be created from such interactions. In this paper, we present our work on two basic building blocks of bipartite quantum protocols, namely, the generation of maximally entangled states and secret key via bipartite quantum interactions. In particular, we provide a non-trivial, efficiently computable upper bound on the positive-partial-transposeassisted (PPT-assisted) quantum capacity of a bipartite quantum interaction. In addition, we provide an upper bound on the secret-key-agreement capacity of a bipartite quantum interaction assisted by local operations and classical communication (LOCC). As an application, we introduce a cryptographic protocol for the read-out of a digital memory device that is secure against a passive eavesdropper.

Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

“…We extend the results in Sect. 4.4 to this general model and demonstrate an improvement to the previous result of the bidirectional max-Rains information (R bi max ) [23]. That is, we show that…”

“…Let Q bi,PPT,↔ and Q bi,PPT,↔, † be the PPT-assisted quantum capacity of a bidirectional channel and its strong converse capacity respectively. 11 It was proved in [23] that…”

Resource theories of multi-time processes: A window into quantum non-Markovianity

“…This could be extended to the multi-time case with discrimination tasks for process tensors. Resource theoretic results on the entanglement of bipartite channels [79,80,[99][100][101] have utilised the idea of quantum strategies [67][68][69][70], which allows for the possibility of dynamical resources being quantum combs. Discrimination of quantum strategies [81] has also been investigated, which involves transformations from strategies to strategies; this is in a similar spirit to our approach of transforming process tensors with superprocesses.…”

How much entanglement can be created in a closed system

“…It evolved from its perception as a mathematical artifact, as a result of EPR paradox [1], to becoming closely related and applicable to the fields of condensed matter [2-7], quantum information [8][9][10][11][12][13][14], quantum metrology [15][16][17][18][19][20], and quantum gravity [21][22][23][24][25].In the field of quantum information, entangled states are the backbone of quantum information protocols as they are considered a resource for tasks such as quantum teleportation [9,26], cryptography [8], and dense coding [27].In these quantum information protocols, more entanglement usually leads to a better performance. Therefore, it is important to set precise upper bounds on how much entanglement is in principle available in performing these tasks [28][29][30][31][32][33][34][35][36][37].As different tasks require different types of entangled states, numerous measures of entanglement have been introduced [38][39][40][41]. An important measure of entanglement is entanglement entropy [33,34,42].…”