Quantum Reading Capacity

The readout of a classical memory can be modelled as a problem of quantum channel discrimination, where a decoder retrieves information by distinguishing the different quantum channels encoded in each cell of the memory [S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In the case of optical memories, such as CDs and DVDs, this discrimination involves lossy bosonic channels and can be remarkably boosted by the use of nonclassical light (quantum reading). Here we generalize these concepts by extending the model of memory from single-cell to multi-cell encoding. In general, information is stored in a block of cells by using a channel-codeword, i.e., a sequence of channels chosen according to a classical code. Correspondingly, the readout of data is realized by a process of “parallel” channel discrimination, where the entire block of cells is probed simultaneously and decoded via an optimal collective measurement. In the limit of an infinite block we define the quantum reading capacity of the memory, quantifying the maximum number of readable bits per cell. This notion of capacity is nontrivial when we suitably constrain the physical resources of the decoder. For optical memories (encoding bosonic channels), such a constraint is energetic and corresponds to fixing the mean total number of photons per cell. In this case, we are able to prove a separation between the quantum reading capacity and the maximum information rate achievable by classical transmitters, i.e., arbitrary classical mixtures of coherent states. In fact, we can easily construct nonclassical transmitters that are able to outperform any classical transmitter, thus showing that the advantages of quantum reading persist in the optimal multi-cell scenario.

💡 Research Summary

The paper revisits the problem of reading classical digital memories by framing it as quantum channel discrimination (QCD). In the original single‑cell model, each memory cell stores a quantum channel chosen from an ensemble Φ = {φₓ, pₓ}, and the reader (Bob) probes the cell with a quantum transmitter state ρ and performs a measurement to infer which channel was written. The error probability depends on the choice of input state and measurement, and can be reduced by using multiple copies (or multimode probes) of the same channel.

The authors extend this framework to a multi‑cell scenario where information is encoded across a block of cells using a classical codeword—a sequence of channels selected according to a classical error‑correcting code. Reading now consists of a parallel discrimination of the entire block: the reader sends a joint multimode quantum state across all cells simultaneously and performs an optimal collective measurement on the joint output. In the limit of an infinitely large block, the authors define the quantum reading capacity (QRC) as the maximal number of bits that can be reliably extracted per cell.

Two versions of the capacity are considered. The unconstrained QRC, with no limits on the physical resources, trivially equals the amount of information originally stored in each cell. The constrained QRC, however, imposes a realistic energy restriction: the mean total number of photons irradiated on each cell, denoted n, is fixed. This constraint is essential for optical memories, where the channels are lossy bosonic (single‑mode) channels.

For the constrained case the authors first derive a lower bound on the capacity achievable with classical transmitters, i.e., arbitrary mixtures of coherent states. They prove that the optimal classical strategy is simply a single coherent state with mean photon number n, and they compute the corresponding Holevo information, denoted χ_c(n), which they call the classical reading capacity.

Next, they construct explicit non‑classical transmitters—including two‑mode squeezed (EPR) states, squeezed vacuum, and Fock states—and show that, for the same energy budget n, these quantum resources yield a higher Holevo information χ_q(n) > χ_c(n). The advantage is most pronounced in the low‑photon regime (n ≈ 1 or less), precisely the regime where quantum reading was previously shown to outperform classical reading in the single‑cell setting. By evaluating error probabilities and applying the Holevo bound, they demonstrate a strict separation between the quantum reading capacity and its classical counterpart, confirming that quantum advantages persist even when optimal collective decoding over an infinite block is allowed.

The paper also discusses practical implications: the separation suggests that future high‑density optical storage devices (e.g., CDs, DVDs, or next‑generation photonic memories) could benefit from quantum illumination techniques, achieving higher data rates or storage densities without increasing the optical power. The authors note that implementing the required non‑classical states and collective measurements is experimentally challenging but within reach of current quantum optics technology (e.g., on‑chip parametric down‑conversion sources and high‑efficiency photon‑number‑resolving detectors).

In conclusion, the work provides a comprehensive theoretical framework for quantum reading in the multi‑cell regime, defines a meaningful capacity measure under realistic energy constraints, and rigorously proves that non‑classical light can surpass any classical strategy. This establishes a solid foundation for future experimental demonstrations and for the design of quantum‑enhanced optical storage systems.