The field of quantum information has been growing fast over the past decade. Optical quantum computation, based on the concepts of KLM and cluster states, has witnessed experimental realizations of larger and more complex systems in terms of photon number. Quantum optical systems, which offer long coherence times and easy manipulation of single qubits, allow us to probe quantum properties of the light itself and of the physical systems around it. Recently, a linear scheme for quantum computing, relying on the bosonic nature of particles, has been proposed and realized experimentally with photons. The ability to efficiently measure superpositions of quantum states consisting of several photons is essential to the characterization of such systems. In fact, the entire field of quantum information completely relies on the ability to recover quantum states from measurements. However, the characterization of quantum states requires many measurements, and often necessitates complicated measurements schemes; for example, characterizing qubits requires measurements. Here, we utilize structure, inherent to physically interesting quantum states of light, in order to reduce the complexity in the recovery of a quantum state. In particular, we devise a method enabling the recovery of three-photon quantum states from only two-fold correlation measurements in a single setting. The ability to take two-fold coincidences instead of three-fold offers the recovery of the quantum states in far less measurements and in a considerably higher SNR, because detection of two-photon events is much more likely than that of three-photon ones. The concept suggested here paves the way to further ideas on structure-based super resolution in quantum state tomography, such as recovering a quantum state in an unknown basis in a single setup and recovering the state of several photons without number resolving detectors.
The field of quantum information has been growing fast over the past decade. Optical quantum computation, based on the concepts of KLM and cluster states, has witnessed experimental realizations of larger and more complex systems in terms of photon number. Quantum optical systems, which offer long coherence times and easy manipulation of single qubits, allow us to probe quantum properties of the light itself and of the physical systems around it. Recently, a linear scheme for quantum computing, relying on the bosonic nature of particles, has been proposed and realized experimentally with photons. The ability to efficiently measure superpositions of quantum states consisting of several photons is essential to the characterization of such systems. In fact, the entire field of quantum information completely relies on the ability to recover quantum states from measurements. However, the characterization of quantum states requires many measurements, and often necessitates complicated measurements schemes; for example, characterizing qubits requires measurements. Here, we utilize structure, inherent to physically interesting quantum states of light, in order to reduce the complexity in the recovery of a quantum state. In particular, we devise a method enabling the recovery of three-photon quantum states from only two-fold correlation measurements in a single setting. The ability to take two-fold coincidences instead of three-fold offers the recovery of the quantum states in far less measurements and in a considerably higher SNR, because detection of two-photon events is much more likely than that of three-photon ones. The concept suggested here paves the way to further ideas on structure-based super resolution in quantum state tomography, such as recovering a quantum state in an unknown basis in a single setup and recovering the state of several photons without number resolving detectors.
Recovery of quantum states from measurements is an essential component in quantum information processing. In quantum optical systems, which naturally offer low decoherence and easy manipulation, quantum states are characterized by correlation measurements. When the states comprise more photons so as to encode more qubits, high-order correlation measurements are required. However, high-order correlations are hard to measure in experiments, as the rate of high-order coincidences decreases very fast when increasing the correlation order. This results in a poor signal-to-noise ratio. Likewise, the number of measurements required to characterize a quantum state increases exponentially with the increase in the number of qubits. Here, we use structure, present in most quantum states of interest (for quantum computing, cryptography, boson sampling, etc.), to recover the full quantum state of three photons from two-fold correlations in a single experimental setup.
Quantum information has been drawing a wealth of research in recent years, shedding light on questions at the heart of quantum mechanics, as well as advancing fields such as complexity theory, cryptography, key distribution, and chemistry. These fundamental and applied aspects of quantum information rely on a crucial issue: the ability to characterize a quantum state from measurements, through a process called Quantum State Tomography (QST). However, QST requires a large number of measurements, each derived from a different physical observable corresponding to a different experimental setup. Unfortunately, changing the setup results in unwanted changes to the data, prolongs the measurement and impairs the assumptions that are always made about the stationarity of the noise. Here, we propose to overcome these drawbacks by performing QST with a single observable. A single observable can often be realized by a single setup, thus considerably reducing the experimental effort. In general, measurements of a single observable do not hold enough information to recover the quantum state. We overcome this lack of information by relying on concepts inspired by Compressed Sensing (CS), exploiting the fact that the sought state - in many applications of quantum information - is close to a pure state (and thus has low rank). Additionally, we increase the system dimension by adding an ancilla that couples to information evolving in the system, thereby providing more measurements, enabling the recovery of the original quantum state from a single-observable measurements. We demonstrate our approach on multi-photon states by recovering structured quantum states from a single observable, in a single experimental setup. We further show how this approach can be used to recover quantum states without number-resolving detectors.
The field of quantum information relies on the crucial issue of characterizing quantum states from measurements. This is performed through a process called quantum state tomography (QST). However, QST requires a large number of measurements, each derived from a different physical observable corresponding to a different experimental setup. Changing the setup results in unwanted changes to the data, prolongs the measurement, and impairs assumptions made about noise. Here, we propose to overcome these drawbacks by performing QST with a single observable. A single observable can often be realized by a single setup, thereby considerably reducing the experimental effort. However, the information contained in a single observable is insufficient for full QST. To overcome the lack of sufficient measurements in a single observable, we increase the system dimension by adding an ancilla that couples to the information in the system and exploit the fact that the sought state is often close to a pure state. We demonstrate our approach on multiphoton states by recovering structured quantum states from a single observable in a single experimental setup.
Over the last sixty years, classical information theory has revolutionized the understanding of the nature of information, and how it can be quantified and manipulated. Quantum information processing extends these lessons to quantum systems, where the properties of intrinsic uncertainty and entanglement fundamentally defy classical explanation. This growing field has many potential applications, including computing, cryptography, communication, and metrology. As inherently mobile quantum particles, photons are likely to play an important role in any mature large-scale quantum information processing system. However, the available methods for producing and detecting complex multi-photon states place practical limits on the feasibility of sophisticated optical quantum information processing experiments. In a typical quantum information protocol, a source first produces an interesting or useful quantum state (or set of states), perhaps involving superposition or entanglement. Then, some manipulations are performed on this state, perhaps involving quantum logic gates which further manipulate or entangle the intial state. Finally, the state must be detected, obtaining some desired measurement result, e.g., for secure communication or computationally efficient factoring. The work presented here concerns the first and last stages of this process as they relate to photons: sources and detectors. Our work on sources is based on the need for optimized non-classical states of light delivered at high rates, particularly of single photons in a pure quantum state. We seek to better understand the properties of spontaneous parameteric downconversion (SPDC) sources of photon pairs, and in doing so, produce such an optimized source. We report an SPDC source which produces pure heralded single photons with little or no spectral filtering, allowing a significant rate enhancement. Our work on detectors is based on the need to reliably measure single-photon states. We have focused on optimizing the detection efficiency of visible light photon counters (VLPCs), a single-photon detection technology that is also capable of resolving photon number states. We report a record-breaking quantum efficiency of 91 +/- 3% observed with our detection system. Both sources and detectors are independently interesting physical systems worthy of study, but together they promise to enable entire new classes and applications of information based on quantum mechanics.
In the case of mixed states ρAB of the composite system A ⊗ B, the previous relation generalizes to ρAB = ∑ k pkρ A k ⊗ρk , where pk are probabilities and ρk ’s (ρk ’s) are generic density matrix of the system A (B). The entanglement derives from “subtle” nonlocal correlations between the parts of a quantum system and combines three basic structural elements of quantum theory: the superposition principle, the quantum non-separability property and the exponential scaling of the state space with the number of partitions. This unique resource can be used to perform computational and cryptographic tasks otherwise impossible with classical systems. An entangled state shared by two or more separated parties is a valuable resource for fundamental quantum protocols, such as quantum teleportation [2], quantum computing [3] and quantum cryptography. By using entangled states we can deeply investigate the nonlocal properties of the quantum world. In fact, an entangled system exhibits correlations between two (or more) parties, which cannot be reproduced by a classical theory or, in general, by a Local Hidden Variables Theory (LHVT). Quantum optics represents an excellent experimental test bench for various novel concepts introduced within the framework of quantum information theory. Quantum states of photons, generally produced by a probabilistic process, namely spontaneous parametric down conversion (SPDC), may be easily and accurately manipulated using linear and nonlinear optical devices and measured by efficient single-photon detectors. Photonic qubits represent the typical carrier of quantum information and can be distributed over long distances, either in free-space or in low-loss optical fibers. Two-particle experiments correspond to operate with qubits belonging to a (2 × 2) Hilbert space. Many quantum information tasks and fundamental tests of quantum mechanics, such as the simulation of properties of quantum systems, the realization of quantum algorithms of increasing complexity and the investigation of the quantum world at a mesoscopic level, deal with a large number of qubits. In order to take full advantage of the possibilities offered by quantum mechanics, more qubits must be added to a quantum state. Two approaches may be followed to increase the number of qubits. The first one consists of increasing the number of entangled particles. In this way, multi-qubit entangled states are created by distributing the qubits between the particles so that each particle carries one qubit. A second strategy consists of encoding more than one qubit in each particle, by exploiting different degrees of freedom (DOFs) of the photon such as the polarization, the path, the emission time, the orbital angular momentum. This has been used to create two-photon fourand six-qubit states and up to five-photon ten-qubit graph states. The entanglement of two particles in different DOFs corresponds to socalled hyperentanglement. It is worth noting that multi-qubit hyperentanglement allows to achieve higher
As single-photon sources become more mature and are used more often in quantum information, communications and measurement applications, their characterization becomes more important. Single-photon-like light is often characterized by its brightness, and two quantum properties: the single-photon composition and the photon indistinguishability. While it is desirable to obtain these quantities from a single measurement, currently two or more measurements are required. Here, we simultaneously determine the brightness, the single photon purity, the indistinguishability, and the statistical distribution of Fock states to third order for a quantum light source. The measurement uses a pair of two-photon (n = 2) number-resolving detectors. n > 2 number-resolving detectors provide no additional advantage in the single-photon characterization. The new method extracts more information per experimental trial than a conventional measurement for all input states, and is particularly more e cient for statistical mixtures of photon states. Thus, using this n=2, number- resolving detector scheme will provide advantages in a variety of quantum optics measurements and systems.