Quantum Reading Capacity: General Definition and Bounds

Abstract

Quantum reading refers to the task of reading out classical information stored in a classical memory. In any such protocol, the transmitter and receiver are in the same physical location, and the goal of such a protocol is to use these devices, coupled with a quantum strategy, to read out as much information as possible from a classical memory, such as a CD or DVD. In this context, a memory cell is a collection of quantum channels that can be used to encode a classical message in a memory. The maximum rate at which information can be read out from a given memory encoded with a memory cell is called the quantum reading capacity of the memory cell. As a consequence of the physical setup of quantum reading, the most natural and general definition for quantum reading capacity should allow for an adaptive operation after each call to the channel, and this is how we define quantum reading capacity in this paper. In general, an adaptive strategy can give a significant advantage over a non-adaptive strategy in the context of quantum channel discrimination, and this is relevant for quantum reading, due to its close connection with channel discrimination. In this paper, we provide a general definition of quantum reading capacity, and we establish several upper bounds on the quantum reading capacity of a memory cell. We also introduce an environment-parametrized memory cell, and we deliver second-order and strong converse bounds for its quantum reading capacity. We calculate the quantum reading capacities for some exemplary memory cells, including a thermal memory cell, a qudit erasure memory cell, and a qudit depolarizing memory cell. We finally provide an explicit example to illustrate the advantage of using an adaptive strategy in the context of zero-error quantum reading capacity.

Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices

“…Definition 4 (Jointly covariant memory cell [DW17]) A set M X = {M x A→B } x∈X of quantum channels is jointly covariant if there exists a group G such that for all x ∈ X , the channel M x is a covariant channel with respect to the group G (cf., Definition 1).…”

“…In subsequent works [PLG + 11, LP17, DW17], the model was extended to a memory cell consisting of arbitrary quantum channels. In [DW17], the most natural and general definition of the reading capacity of a memory cell was given, and this work also determined the reading capacities for some broad classes of memory cells. Quantum reading can be understood as a direct application of quantum channel discrimination [Kit97, Fuj01, DPP01, Aci01, WY06, DFY09, HHLW10, CMW16, DGLL16].…”

“…The private reading task comprises the estimation of the secret message encoded in the form of a sequence of quantum wiretap channels chosen from a given set {M x B →BE } x∈X of quantum wiretap channels (called a wiretap memory cell), where X is an alphabet, such that there is negligible leakage of information to Eve, who has access to the system E. A special case of this is when each wiretap channel M x B →BE is an isometric channel. In the most natural and general setting, the reader can use an adaptive strategy when decoding, as considered in [DW17]. which may also be known to Eve, before executing the reading protocol.…”

“…As argued in [DW17], based on the physical setup of quantum reading, in which the reader assumes the role of both a transmitter and receiver, it is natural to consider the use of an adaptive strategy when defining the private reading capacity of a memory cell.…”

“…The main goal of this section is to evaluate the private reading capacity of the qudit erasure wiretap memory cell [DW17].…”