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We present optimal schemes, based on photon number measurements, for Gaussian state tomography and for Gaussian process tomography. An n-mode Gaussian state is completely specified by 2n^2 +3n parameters. Our scheme requires exactly 2n^2 +3n distinct photon number measurements to tomograph the state and is therefore optimal. Further, we describe an optimal scheme to characterize Gaussian processes by using coherent state probes and photon number measurements.

Quantum 2020

Optimal characterization of Gaussian states and Gaussian channels using photon-number- resolving detectors

photon-number-resolving-detectors

tomography

continuous variable systems

The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
Quantum computing and quantum simulation;
Quantum sensing, metrology and imaging;
Quantum information theory, software and algorithms;
Quantum foundations;
Quantum technology in industry.
The four-day event featured talks from world-renowned scientists, interactive poster sessions and two exciting panel discussions on the themes of Quantum Technology in Industry and Quantum Technology Programmes Around the World.


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The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.

Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. 

poster

Quantum key distribution is a pioneering scheme in the quantum cryptography. On the other hand, quantum direct secure communication scheme shows the possibility of transferring the secret information without the need for a secure key. It is known that bell states are extensively employed to achieve bidirectional quantum communication. While most of the quantum communication protocols revolves around the controller, who prepares and shares the bell states with the communicants, recently controller independent bidirectional quantum communication has been proposed [1]. In the proposed scheme, the sender and the receiver become empowered to generate bell states and hence the role of controller becomes insignificant. Further, the protocol is modified so as to use non-maximally entangled states [2]. The protocol is shown to be secure against intercept and resend attack. As the non-maximally entangled states are relatively easy to realize in comparison with maximally entangled states, controller independent protocol becomes physically feasible. 

(1) Mohapatra, A.K., Balakrishnan, S.: Controller-independent bidirectional quantum direct communication. Quantum Inf. Process. 16, 147 (2017)
(2) Akaash, S., Balakrishnan, S.: Controller-independent quantum bidirectional communication using non-maximally entangled states. Quantum Inf. Process. 19, 133 (2020)

The poster is essentially a summary of the results presented in the aforementioned papers. More technical details can be found in the papers.


Insignificant controller in the quantum communication protocols

Understanding what happens to a qubit thrown into a black hole is not an easy task; is the information lost to any outside observer or can it be retrieved by local measurements? This problem boils down to studying the scrambling of information over the event horizon, which draws attention to a general class of problems: scrambling of quantum information. In our work, we study the scrambling properties of quantum systems through the mutual information (MI). To this end, we lower bound the MI by the Out-of- Time-Order Correlators (OTOC) and determine its dynamical properties, relating the MI to thermodynamic quantities such as irreversible entropy production. We then illustrate, through examples, the thermodynamic significance of the MI for quantum information scrambling. Thus, as a main result, we establish a clear link between the MI and the OTOC, which enables us to probe the thermodynamics of quantum information scrambling and opens the door for further studies of the thermodynamics of quantum chaotic systems.

Quantum scrambling and the growth of mutual information

In this work, we analyze the concept of quantum bridge to achieve Quantum Teleportation (QT) and propose two schemes for QT using an Non-Maximally Entangled (NME) channel as a bridge between the sender and the receiver. In the rst scheme, QT is achieved by the application of unitary operator. Here the probability of success does not change even if we interchange the Degree of Entanglement (DoE) of the quantum channels. In the second scheme, generalized Bell basis measurements are utilized to achieve successful QT. Here, successful QT is achieved under two situations: (i) the DoE of channels and measurements are the same, pairwise and (ii) the DoE of the channels are the same, and the DoE of the measurements are the same. We show that quantum channels and the measurements are equivalent in achieving the QT only when the DoE is the maximum.

Quantum Teleportation: A Perspective from the Degree of Entanglement

Indefinite causal order has shown improvements for quantum communication where the channels used along the process are very noisy, thus being able to obtain improved transmission rates. Following such trend, it has also been studied the improvements obtained in teleportation as a genuine communication channel when the entangled resource is imperfect. It induces naturally a Pauli channel well characterized as function of the characteristic parameters of the entangled resource. We show that with more than two channels in superposition of causal order, the fidelity of teleportation improves, despite the probability of stochastic process due to the involvement of post-measurement shows a progressive decrease. In this work, we tackle the problem when two or more channels are applied under indefinite causal order, then analyzing the fidelity thus observing that the probability of successful transmission becomes compromised with the grown of channels. Then, a novel approach with the assistance of a weak measurement is analyzed in order to correct such loss. The weak measurement is aimed to select the best configuration for the channel in order to improve such probability with loss for the fidelity of transmission.

Improving imperfect quantum teleportation with indefinite causal order assisted by post-measurement and weak measurement

Heralded single photons emitted from spontaneous four-wave mixing process in a cold atomic cloud have extremely long coherence time up to microseconds, due to slow light effect of electromagnetically induced transparency (EIT). The temporal state of these single photons is typically characterized by the photon counting approach. For the first time, we utilize balanced homodyne tomography (BHT) to fully characterize the temporal state. From reconstructing its density matrix, and further verify that the temporal state shaped through EIT window is pure. To further improve the mode matching between the optical field of Anti-Stokes and the local field in BHT, the driving beam of EIT is split from the local field, and frequency shifted using an electric-optic modulator. The characterization of the pure temporal-spectral state of the single photons paves the way for exploiting the temporal-spectral degree of freedom to develop photonic-quantum information processing.

Tomography of the pure temporal state of single photons from a cold atomic ensemble

We study the classical analog of the quantum metric tensor for two well known models in atomic and nuclear physics. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and quantum metrics in the thermodynamic limit and compute their scalar curvatures, finding that they are continuous across the phase transition when there is no resonance, and that they diverge in the same way under resonance. Second, we compute the classical and quantum metrics for the Lipkin-Meshkov-Glick model in the thermodynamic limit and find a perfect agreement between them. Finally, we complement the analytic results with a finite-size numerical analysis.

Classical and quantum perspectives of the parameter space geometry in the Dicke and Lipkin models

This paper argues that the “Measurement Problem” is foundationally moot, using the abstraction of “Color Guessing Game”. It has been reasoned that the preferred question to ask is, once taken the measurement, what is the certainty that the measured physical state of quantum system is the original intended state governed by absolute laws of nature. The certainty of the measured state |ϕ_k〉 of the physical system with wave function |ψ〉=∑_i〖c_i |ϕ_i〉〗 being the original intended state is given by P(|ϕ_k〉)_certainty=[|c_k |^2/(∑_i|c_i |^2 )]∙[|c_k |^2/(∑_j|c_j |^2 ) ]_measurement, given that the measurement probe’s wave function interaction with |ψ〉 is unknown. It has been argued that measured state’s interactions with other quantum system corresponds to classical reality, which can be changed by the act of measurement.

The Problem with 'The Measurement Problem'

Designing band structures through the application of coherent time-periodic drives applied to quantum systems of reduced dimensions is a powerful experimental tool for inducing novel out-of-equilibrium quantum phases. In our work, we study an effect of the high-order harmonics generation in currents flowing through a quantum ring, being under the influence of an external microwave field and coupled to one or two reservoirs biased with a voltage periodic in time. The proposed technique that can be tunable by the joint action of a sine-wave voltage bias and microwave pumping permits to implement a simple detection system of microwaves as well as novel practically useful nanoscale setups with a discrete structure in the frequency domain. Fundamental quantum laws governing the system guarantee existence, identification and more stability under change of its states. We discuss possible realizations of the proposed device and analyze from this viewpoint results of recent experiments on equilibrium charge transport in AlxGa1-xAs/GaAs based quantum rings.

Tailoring high-harmonic generation from a phase-coherent quantum ring

Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called "second laws of thermodynamics" do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst.

All states are universal catalysts in quantum thermodynamics

Binning a continuous degree of freedom of one particle creates an effective, finite-dimensional qudit. Photonic time-bin qubits and qudits are popular [1,2,3], though efficiently processing high-dimensional time-bins remains challenging. In this theoretical work, we devise a scheme using a single, binned degree of freedom of one particle as a system of multiple, effective qubits. Distinct qubits correspond to scales of the original, continuous variable. While general bin processing overhead scales polynomially with dimension [4,5], efficient quantum algorithms implemented on multi-qubit time-bins may use polynomial-size circuits optimized for conventional, multi-qubit quantum computing. Considering scales below accessible precision, we find intriguing analogies to infinite-dimensional von Neumann algebras. Finally, scale-separated qubits present an experimentally accessible medium to probe the quantum-classical transition of chaos.

[1] Bussieres et al. 2006. arXiv:quant-ph/0608183

[2] Islam et al. 2017 Sci. Adv. doi:10.1126/sciadv.1701491

[3] Victora et al. 2019. Quantum Photonics: Pioneering Advances and Emerging Applications, pp 179-206. doi:10.1007/978-3-319-98402-5_5

[4] Reck et al. 1994. Phys. Rev. Lett. doi:10.1103/PhysRevLett.73.58

[5] Kumar & Dhand. 2020. arXiv:2001.02012

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Optimal characterization of Gaussian states and Gaussian channels using photon-number- resolving detectors

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