Lorenzo Maccone

Quantum-enhanced measurements: beating the standard quantum limit.

Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ “quantum tricks” such as squeezing and entanglement.

Advances in quantum metrology

The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections.

Classical Capacity of the Lossy Bosonic Channel: The Exact Solution

The classical capacity of the lossy bosonic channel is calculated exactly. It is shown that its Holevo information is not superadditive, and that a coherent-state encoding achieves capacity. The capacity of far-field, free-space optical communications is given as an example.

Quantum-enhanced positioning and clock synchronization

A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. The accuracy of such procedures is classically limited by the available power and bandwidth. Quantum entanglement and squeezing have been exploited in the context of interferometry, frequency measurements, lithography and algorithms. Here we report that quantum entanglement and squeezing can also be employed to overcome the classical limits in procedures such as positioning systems, clock synchronization and ranging. Our use of frequency-entangled pulses to construct quantum versions of these protocols results in enhanced accuracy compared with their classical analogues. We describe in detail the problem of establishing a position with respect to a fixed array of reference points.

Quantum illumination with Gaussian states.

An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum-illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric down-conversion. By making the optimum joint measurement on the light received from the target region together with the retained spontaneous parametric down-conversion idler beam, the quantum-illumination system realizes a 6 dB advantage in the error-probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.

Quantum limits to dynamical evolution

We establish the minimum time it takes for an initial state of mean energy E and energy spread {delta}E to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial and final states. In this context, we study the role of entanglement among subsystems in speeding up the dynamics of a composite system.

Quantum random access memory.

A random access memory (RAM) uses n bits to randomly address N=2(n) distinct memory cells. A quantum random access memory (QRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.

Quantum Private Queries

We propose a cheat sensitive quantum protocol to perform a private search on a classical database which is efficient in terms of communication complexity. It allows a user to retrieve an item from the database provider without revealing which item he or she retrieved: if the provider tries to obtain information on the query, the person querying the database can find it out. The protocol ensures also perfect data privacy of the database: the information that the user can retrieve in a single query is bounded and does not depend on the size of the database. With respect to the known (quantum and classical) strategies for private information retrieval, our protocol displays an exponential reduction in communication complexity and in running-time computational complexity.

Minimum output entropy of bosonic channels: A conjecture

The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture—that output states resulting from coherent-state inputs majorize the output states from other inputs—is also discussed. presented. We also consider a stronger conjecture—that out- put states resulting from coherent-state inputs majorize the output states from other inputs—which, if true, would imply the minimum output entropy conjecture. (Note that the mini- mum output entropy problem was previously treated in (7), which reported some of the results that we will discuss.) Additional supporting evidence for the minimum-entropy conjecture appears in our companion paper (8), where we show that the integer-order Renyi entropies and the Wehrl entropy at the output of the bosonic channel are minimized when the channel input is a coherent state. In Sec. II we present CP maps for the two bosonic chan- nels that will be considered in this paper. The minimum out- put entropy conjecture and its stronger (majorization) version are then stated and explained. In Sec. III we analyze the two channel maps in detail, and develop some useful properties of their output entropies. In Sec. IV we prove the minimum output entropy conjecture for the restricted scenario in which only Gaussian states may be fed into the channel. In Sec. V we present a collection of lower bounds on S. These lower bounds are consistent with the minimum output entropy con- jecture. Moreover, in the low- and high-noise regimes they approach asymptotically the upper bounds from which the conjecture arises. In Sec. VI we obtain necessary conditions on any input state that minimizes the output entropy. We demonstrate, in particular, that every coherent-state input produces an output state that achieves a local minimum of the output entropy. Finally, in Sec. VII we address the stron- ger version of the conjecture by exhibiting some evidence that output states produced by coherent-state inputs majorize all other output states. The paper is structured so that Secs. IV and VII may be read independently. The most technical parts of the derivations have been relegated to the Appendi- ces.

Using entanglement against noise in quantum metrology.

We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that external ancillas are useless. This changes in the presence of noise; here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrology strategies in the presence of noise.