Quantum and Classical Message Identification via Quantum Channels

We discuss concepts of message identification in the sense of Ahlswede and Dueck via general quantum channels, extending investigations for classical channels, initial work for classical-quantum (cq) channels and "quantum fingerprinting". We show that the identification capacity of a discrete memoryless quantum channel for classical information can be larger than that for transmission; this is in contrast to all previously considered models, where it turns out to equal the common randomness capacity (equals transmission capacity in our case): in particular, for a noiseless qubit, we show the identification capacity to be 2, while transmission and common randomness capacity are 1. Then we turn to a natural concept of identification of quantum messages (i.e. a notion of "fingerprint" for quantum states). This is much closer to quantum information transmission than its classical counterpart (for one thing, the code length grows only exponentially, compared to double exponentially for classical identification). Indeed, we show how the problem exhibits a nice connection to visible quantum coding. Astonishingly, for the noiseless qubit channel this capacity turns out to be 2: in other words, one can compress two qubits into one and this is optimal. In general however, we conjecture quantum identification capacity to be different from classical identification capacity.Comment: 18 pages, requires Rinton-P9x6.cls. On the occasion of Alexander Holevo's 60th birthday. Version 2 has a few theorems knocked off: Y Steinberg has pointed out a crucial error in my statements on simultaneous ID codes. They are all gone and replaced by a speculative remark. The central results of the paper are all unharmed. In v3: proof of Proposition 17 corrected, without change of its statemen

Strong Converse for Identification via Quantum Channels

In this paper we present a simple proof of the strong converse for identification via discrete memoryless quantum channels, based on a novel covering lemma. The new method is a generalization to quantum communication channels of Ahlswede's recently discovered appoach to classical channels. It involves a development of explicit large deviation estimates to the case of random variables taking values in selfadjoint operators on a Hilbert space. This theory is presented separately in an appendix, and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems.Comment: 11 pages, LaTeX2e, requires IEEEtran2e.cls. Some errors and omissions corrected, references update

Identification via Quantum Channels in the Presence of Prior Correlation and Feedback

Continuing our earlier work (quant-ph/0401060), we give two alternative proofs of the result that a noiseless qubit channel has identification capacity 2: the first is direct by a "maximal code with random extension" argument, the second is by showing that 1 bit of entanglement (which can be generated by transmitting 1 qubit) and negligible (quantum) communication has identification capacity 2. This generalises a random hashing construction of Ahlswede and Dueck: that 1 shared random bit together with negligible communication has identification capacity 1. We then apply these results to prove capacity formulas for various quantum feedback channels: passive classical feedback for quantum-classical channels, a feedback model for classical-quantum channels, and "coherent feedback" for general channels.Comment: 19 pages. Requires Rinton-P9x6.cls. v2 has some minor errors/typoes corrected and the claims of remark 22 toned down (proofs are not so easy after all). v3 has references to simultaneous ID coding removed: there were necessary changes in quant-ph/0401060. v4 (final form) has minor correction

Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels

We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be equivalent to a coding theorem for rate distortion under a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan, arXiv:2302.00625]. Both one-shot results directly yield corollaries about the i.i.d. asymptotics, in terms of the coherent information of the channel. The power of our quantum covering lemma is demonstrated by two additional applications: first, we formulate a quantum channel resolvability problem, and provide one-shot as well as asymptotic upper and lower bounds. Secondly, we provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels, in particular separating for the first time the simultaneous identification capacity from the unrestricted one, proving a long-standing conjecture of the last author.Comment: 29 pages, 3 figures; v2 fixes an error in Definition 6.1 and various typos and minor issues throughou

Quantum Process Estimation via Generic Two-Body Correlations

Performance of quantum process estimation is naturally limited to fundamental, random, and systematic imperfections in preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction due to the fact that standard data analysis techniques presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty state generators and analyzers. Specifically, we present a generalization of "Direct Characterization of Quantum Dynamics" [M. Mohseni and D. A. Lidar, Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that, for several physically relevant noisy preparations and measurements, only classical correlations and small data processing overhead are sufficient to accomplish the full system identification. Furthermore, we provide the optimal input states for which the error amplification due to inversion on the measurement data is minimal.Comment: 7 pages, 2 figure