There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

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Gaussian quantum information

The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted a considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has only been initiated recently. In this Colloquium we discuss and review the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

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Colloquium: quantum coherence as a resource

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

/pdf/gaussian-quantum-information-3johze75r1.pdf

Quantum properties are soon subject to decoherence once the quantum system interacts with the classical environment. In this paper we experimentally test how propagation losses, in a Gaussian channel, affect the bipartite Gaussian entangled state generated by a subthreshold type-II optical parametric oscillator. Experimental results are discussed in terms of different quantum markers, as teleportation fidelity, quantum discord, and mutual information, and continuous-variable (CV) entanglement criteria. To analyze state properties we have retrieved the composite system covariance matrix by a single homodyne detector. We experimentally found that, even in the presence of a strong decoherence, the generated state never disentangles and keeps breaking the quantum limit for the discord. This result proves that the class of CV entangled states discussed in this paper would allow, in principle, to realize quantum teleportation over an infinitely long Gaussian channel.

Experimental analysis of decoherence in continuous-variable bipartite systems

Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we describe in detail and experimentally demonstrate a robust and reliable method to fully characterize bipartite optical Gaussian states by means of a single homodyne detector. We have successfully applied our method to the bipartite states generated by a sub-threshold type-II optical parametric oscillator which produces a pair of thermal cross-polarized entangled cw frequency degenerate beams. The method provides a reliable reconstruction of the covariance matrix and allows us to retrieve all the physical information about the state under investigation. These include observable quantities, such as energy and squeezing, as well as nonobservable ones such as purity, entropy, and entanglement. Our procedure also includes advanced tests for the Gaussianity of the state and, overall, represents a powerful tool to study the bipartite Gaussian state from the generation stage to the detection one.

Quantum characterization of bipartite Gaussian states

In quantum reading, a quantum state of light (transmitter) is applied to read classical information. In the presence of noise or for sufficiently weak signals, quantum reading can outperform classical reading by reason of enhanced state distinguishability. Here we show that enhanced quantum efficiency depends on the presence in the transmitter of a particular type of quantum correlations, the discord of response. Different encodings and transmitters give rise to different levels of efficiency. Considering noisy quantum probes, we show that squeezed thermal transmitters with non-symmetrically distributed noise among the field modes yield higher quantum efficiency compared with coherent thermal quantum states. The noise-enhanced quantum advantage is a consequence of the discord of response being a non-decreasing function of increasing thermal noise under constant squeezing, a behavior that leads to increased state distinguishability. We finally show that, for non-symmetric squeezed thermal states, the probability of error, as measured by the quantum Chernoff bound, vanishes asymptotically with increasing local thermal noise with finite global squeezing. Therefore, with fixed finite squeezing, noisy but strongly discordant quantum states with a large noise imbalance between the field modes can outperform noisy classical resources as well as pure entangled transmitters with the same finite level of squeezing.

Device-independent quantum reading and noise-assisted quantum transmitters

In quantum reading, a quantum state of light (transmitter) is applied to read classical information. In the presence of noise or for sufficiently weak signals, quantum reading can outperform classical reading by enhanced state distinguishability. Here we show that the enhanced quantum efficiency depends on the presence in the transmitter of a particular type of quantum correlations, the discord of response. Different encodings and transmitters give rise to different levels of efficiency. Considering noisy quantum probes we show that squeezed thermal transmitters with non-symmetrically distributed noise among the field modes yield a higher quantum efficiency compared to coherent thermal quantum states. The noise-enhanced quantum advantage is a consequence of the discord of response being a non-decreasing function of increasing thermal noise under constant squeezing, a behavior that leads to an increased state distinguishability. We finally show that, for non-symmetric squeezed thermal states, the probability of error, as measured by the quantum Chernoff bound, vanishes asymptotically with increasing local thermal noise at finite global squeezing. Therefore, at fixed finite squeezing, noisy but strongly discordant quantum states with large noise imbalance between the field modes can outperform noisy classical resources as well as pure entangled transmitters with the same finite level of squeezing.

We introduce and discuss a set of tunable two-mode states of continuous-variable systems, as well as an efficient scheme for their experimental generation. This novel class of tunable entangled resources is defined by a general ansatz depending on two experimentally adjustable parameters. It is very ample and flexible as it encompasses Gaussian as well as non-Gaussian states. The latter include, among others, known states such as squeezed number states and de-Gaussified photon-added and photon-subtracted squeezed states, the latter being the most efficient non-Gaussian resources currently available in the laboratory. Moreover, it contains the classes of squeezed Bell states and even more general non-Gaussian resources that can be optimized according to the specific quantum technological task that needs to be realized. The proposed experimental scheme exploits linear optical operations and photon detections performed on a pair of uncorrelated two--mode Gaussian squeezed states. The desired non-Gaussian state is then realized via ancillary squeezing and conditioning. Two independent, freely tunable experimental parameters can be exploited to generate different states and to optimize the performance in implementing a given quantum protocol. As a concrete instance, we analyze in detail the performance of different states considered as resources for the realization of quantum teleportation in realistic conditions. For the fidelity of teleportation of an unknown coherent state, we show that the resources associated to the optimized parameters outperform, in a significant range of experimental values, both Gaussian twin beams and photon-subtracted squeezed states.

Daniela Buono

Papers

Experimental analysis of decoherence in continuous-variable bipartite systems

Quantum characterization of bipartite Gaussian states

Device-independent quantum reading and noise-assisted quantum transmitters

Device-independent quantum reading and noise-assisted quantum transmitters

Tunable non-Gaussian resources for continuous-variable quantum technologies