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

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

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

Strong Converse and Second-Order Asymptotics of Channel Resolvability

We study the problem of channel resolvability for fixed i.i.d. input distributions and discrete memoryless channels (DMCs), and derive the strong converse theorem for any DMCs that are not necessarily full rank. We also derive the optimal second-order rate under a condition. Furthermore, under the condition that a DMC has the unique capacity achieving input distribution, we derive the optimal second-order rate of channel resolvability for the worst input distribution.Comment: 7 pages, a shorter version will appear in ISIT 2014, this version includes the proofs of technical lemmas in appendice

Quantum Channels and Simultaneous ID Coding

This paper is on identification of classical information by the use of quantum channels. We focus on simultaneous ID codes which use measurements being useful to identify an arbitrary message. We give a direct and a converse part of the appropriate coding theorem.Comment: 15 page

On converse bounds for classical communication over quantum channels

We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical communication can be achieved by activated, no-signalling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new efficiently computable meta-converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel. As applications, we provide a finite resource analysis of classical communication over quantum erasure channels, including the second-order and moderate deviation asymptotics. Third, we explore the asymptotic analogue of our new meta-converse, the $\Upsilon$-information of the channel. We show that its regularization is an upper bound on the classical capacity, which is generally tighter than the entanglement-assisted capacity and other known efficiently computable strong converse bounds. For covariant channels we show that the $\Upsilon$-information is a strong converse bound.Comment: v3: published version; v2: 18 pages, presentation and results improve

Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels

Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled encoding schemes, but this is not always the case. In this paper, we prove that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter. In doing so, we identify a bound on the strong converse exponent, which determines the exponentially decaying rate at which the success probability tends to zero, for a sequence of codes with communication rate exceeding capacity. Proving a strong converse, along with an achievability theorem, shows that the classical capacity is a sharp boundary between reliable and unreliable communication regimes. One of the main tools in our proof is the sandwiched Renyi relative entropy. The same method of proof is used to derive an exponential bound on the success probability when communicating over an arbitrary quantum channel assisted by classical feedback, provided that the transmitter does not use entangled encoding schemes.Comment: 24 pages, 2 figures, v4: final version accepted for publication in Problems of Information Transmissio