Local Quantum Measurement and No-Signaling Imply Quantum Correlations

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.Comment: Published version. 5 pages, 1 figure

A violation of the uncertainty principle implies a violation of the second law of thermodynamics

Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? We give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.Comment: 8 pages, revte

Compressibility of Mixed-State Signals

We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a decomposition of the Hilbert space into the redundant part and the irreducible part. After removing the redundancy, the optimal compression rate is shown to be given by the von Neumann entropy of the reduced ensemble.Comment: 7 pages, no figur

Quantum channels with a finite memory

In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no nformation is lost to the environment, achieving the upper bound implies that the channel is asymptotically noiseless.Comment: 7 Pages, RevTex, Jrnl versio

The quantum capacity is properly defined without encodings

We show that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information. This allows us to use the coherent information maximized over all sources and and block sizes, but not encodings, to bound the quantum capacity. We perform an explicit calculation of this maximum coherent information for the quantum erasure channel and apply the bound in order find the erasure channel's capacity without relying on an unproven assumption as in an earlier paper.Comment: 19 pages revtex with two eps figures. Submitted to Phys. Rev. A. Replaced with revised and simplified version, and improved references, etc. Why can't the last line of the comments field end with a period using this web submission form

Generalized remote state preparation: Trading cbits, qubits and ebits in quantum communication

We consider the problem of communicating quantum states by simultaneously making use of a noiseless classical channel, a noiseless quantum channel and shared entanglement. We specifically study the version of the problem in which the sender is given knowledge of the state to be communicated. In this setting, a trade-off arises between the three resources, some portions of which have been investigated previously in the contexts of the quantum-classical trade-off in data compression, remote state preparation and superdense coding of quantum states, each of which amounts to allowing just two out of these three resources. We present a formula for the triple resource trade-off that reduces its calculation to evaluating the data compression trade-off formula. In the process, we also construct protocols achieving all the optimal points. These turn out to be achievable by trade-off coding and suitable time-sharing between optimal protocols for cases involving two resources out of the three mentioned above.Comment: 15 pages, 2 figures, 1 tabl

Environment and classical channels in categorical quantum mechanics

We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the earlier introduced axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.Comment: 26 pages, many pics; this third version has substantially more explanations than previous ones; Journal reference is of short 14 page version; Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL), Lecture Notes in Computer Science 6247, Springer-Verlag (2010

Entangling quantum measurement and its properties

We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable system and apparatus. It is shown that the coherent information can be effectively used for the analysis of such entangling measurements whose possible applications are discussed as well.Comment: 8 pages, 1 figure; accepted for publication in Phys. Rev.

Trading quantum for classical resources in quantum data compression

We study the visible compression of a source E of pure quantum signal states, or, more formally, the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity, when the compressor is given the identity of the input state sequence as classical information. According to the quantum source coding theorem, the optimal quantum rate is the von Neumann entropy S(E) qubits per signal. We develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified separately. This leads to a trade--off curve Q(R), where Q(R) qubits per signal is the optimal quantum rate for a given classical rate of R bits per signal. Our main result is an explicit characterization of this trade--off function by a simple formula in terms of only single signal, perfect fidelity encodings of the source. We give a thorough discussion of many further mathematical properties of our formula, including an analysis of its behavior for group covariant sources and a generalization to sources with continuously parameterized states. We also show that our result leads to a number of corollaries characterizing the trade--off between information gain and state disturbance for quantum sources. In addition, we indicate how our techniques also provide a solution to the so--called remote state preparation problem. Finally, we develop a probability--free version of our main result which may be interpreted as an answer to the question: ``How many classical bits does a qubit cost?'' This theorem provides a type of dual to Holevo's theorem, insofar as the latter characterizes the cost of coding classical bits into qubits.Comment: 51 pages, 7 figure

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39