16,727 research outputs found
Achieving minimum-error discrimination of an arbitrary set of laser-light pulses
Laser light is widely used for communication and sensing applications, so the
optimal discrimination of coherent states--the quantum states of light emitted
by a laser--has immense practical importance. However, quantum mechanics
imposes a fundamental limit on how well different coher- ent states can be
distinguished, even with perfect detectors, and limits such discrimination to
have a finite minimum probability of error. While conventional optical
receivers lead to error rates well above this fundamental limit, Dolinar found
an explicit receiver design involving optical feedback and photon counting that
can achieve the minimum probability of error for discriminating any two given
coherent states. The generalization of this construction to larger sets of
coherent states has proven to be challenging, evidencing that there may be a
limitation inherent to a linear-optics-based adaptive measurement strategy. In
this Letter, we show how to achieve optimal discrimination of any set of
coherent states using a resource-efficient quantum computer. Our construction
leverages a recent result on discriminating multi-copy quantum hypotheses
(arXiv:1201.6625) and properties of coherent states. Furthermore, our
construction is reusable, composable, and applicable to designing
quantum-limited processing of coherent-state signals to optimize any metric of
choice. As illustrative examples, we analyze the performance of discriminating
a ternary alphabet, and show how the quantum circuit of a receiver designed to
discriminate a binary alphabet can be reused in discriminating multimode
hypotheses. Finally, we show our result can be used to achieve the quantum
limit on the rate of classical information transmission on a lossy optical
channel, which is known to exceed the Shannon rate of all conventional optical
receivers.Comment: 9 pages, 2 figures; v2 Minor correction
Quantum Stopwatch: How To Store Time in a Quantum Memory
Quantum mechanics imposes a fundamental tradeoff between the accuracy of time
measurements and the size of the systems used as clocks. When the measurements
of different time intervals are combined, the errors due to the finite clock
size accumulate, resulting in an overall inaccuracy that grows with the
complexity of the setup. Here we introduce a method that in principle eludes
the accumulation of errors by coherently transferring information from a
quantum clock to a quantum memory of the smallest possible size. Our method
could be used to measure the total duration of a sequence of events with
enhanced accuracy, and to reduce the amount of quantum communication needed to
stabilize clocks in a quantum network.Comment: 10 + 5 pages, 3 figure
The Role of Relative Entropy in Quantum Information Theory
Quantum mechanics and information theory are among the most important
scientific discoveries of the last century. Although these two areas initially
developed separately it has emerged that they are in fact intimately related.
In this review I will show how quantum information theory extends traditional
information theory by exploring the limits imposed by quantum, rather than
classical mechanics on information storage and transmission. The derivation of
many key results uniquely differentiates this review from the "usual"
presentation in that they are shown to follow logically from one crucial
property of relative entropy. Within the review optimal bounds on the speed-up
that quantum computers can achieve over their classical counter-parts are
outlined using information theoretic arguments. In addition important
implications of quantum information theory to thermodynamics and quantum
measurement are intermittently discussed. A number of simple examples and
derivations including quantum super-dense coding, quantum teleportation,
Deutsch's and Grover's algorithms are also included.Comment: 40 pages, 11 figure
Distinguishability of States and von Neumann Entropy
Consider an ensemble of pure quantum states |\psi_j>, j=1,...,n taken with
prior probabilities p_j respectively. We show that it is possible to increase
all of the pairwise overlaps || i.e. make each constituent pair
of the states more parallel (while keeping the prior probabilities the same),
in such a way that the von Neumann entropy S is increased, and dually, make all
pairs more orthogonal while decreasing S. We show that this phenomenon cannot
occur for ensembles in two dimensions but that it is a feature of almost all
ensembles of three states in three dimensions. It is known that the von Neumann
entropy characterises the classical and quantum information capacities of the
ensemble and we argue that information capacity in turn, is a manifestation of
the distinguishability of the signal states. Hence our result shows that the
notion of distinguishability within an ensemble is a global property that
cannot be reduced to considering distinguishability of each constituent pair of
states.Comment: 18 pages, Latex, 2 figure
Classical, quantum and total correlations
We discuss the problem of separating consistently the total correlations in a
bipartite quantum state into a quantum and a purely classical part. A measure
of classical correlations is proposed and its properties are explored.Comment: 10 pages, 3 figure
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