Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.

Quantum network coding

Abstract: Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its classical counterpart is another good example to show that digital information flow can be done much more efficiently than conventional (say, liquid) flow. Our answer to the question is similar to the case of cloning, namely, it is shown that quantum network coding is possible if approximation is allowed, by using a simple network model called Butterfly. In this network, there are two flow paths, s1 to t1 and s2 to t2, which shares a single bottleneck channel of capacity one. In the classical case, we can send two bits simultaneously, one for each path, in spite of the bottleneck. Our results for quantum network coding include: (i) We can send any quantum state |ψ1〉 from s1 to t1 and |ψ2〉 from s2 to t2 simultaneously with a fidelity strictly greater than 1/2. (ii) If one of |ψ1〉 and |ψ2〉 is classical, then the fidelity can be improved to 2/3. (iii) Similar improvement is also possible if |ψ1〉 and |ψ2〉 are restricted to only a finite number of (previously known) states. (iv) Several impossibility results including the general upper bound of the fidelity are also given.

Lower bound for accessible information in quantum mechanics.

Abstract: It has long been known that the von Neumann entropy S is an upper bound on the information one can extract from a quantum system in an unknown pure state. In this paper we define the ``subentropy'' Q, which we prove to be a lower bound on this information. Moreover, just as the von Neumann entropy is the best upper bound that depends only on the density matrix, we show that Q is the best lower bound that depends only on the density matrix. Other parallels between S and Q are also demonstrated.

Capacity theorems for quantum multiple-access channels: classical-quantum and quantum-quantum capacity regions

Abstract: In this paper, we consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multiletter characterizations of two different two-dimensional capacity regions. The first region comprises the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.

On Some Additivity Problems in Quantum Information Theory

Abstract: A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity", and the "maximal output purity". All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture.

Multi-dimensional visualization of temporal information

Abstract: Various kinds of business and other information are tracked in real time. A coherent information visualization, for example as a time line, automatically, simultaneously presents relevant information to a user across multiple dimensions. Tools are provided that allow the user to establish and manipulate multi-dimensional linkages to develop insights into information gathered from multiple domains.