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We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or may not be entangled. By performing measurements with multiple different detector settings, we are able to detect correlated errors between two single-qubit measurements performed in different locations. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures describing the detectors are known. The only other needed information is experimentally measured expectation values, which are analyzed for self-consistency. This demonstrates that loop SPAM tomography is a useful technique for detecting errors that would degrade the performance of multiple-qubit quantum information processors.

Whereas in standard quantum-state tomography one estimates an unknown state by performing various measurements with known devices, and whereas in detector tomography one estimates the positive-operator-valued- measurement elements of a measurement device by subjecting to it various known states, we consider here the case of SPAM (state preparation and measurement) tomography where neither the states nor the measurement device are assumed known. For (f-dimensional systems measured by d-outcome detectors, we find there are at most d2(d2 - 1) "gauge" parameters that can never be determined by any such experiment, irrespective of the number of unknown states and unknown devices. For the case d = 2 we find gauge-invariant quantities that can be accessed directly experimentally and that can be used to detect and describe SPAM errors. In particular, we identify conditions whose violations detect the presence of correlations between SPAM errors. From the perspective of SPAM tomography, standard quantum-state tomography and detector tomography are protocols that fix the gauge parameters through the assumption that some set of fiducial measurements is known or that some set of fiducial states is known, respectively. [ABSTRACT FROM AUTHOR]

We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon time-dependent spectrum reveals the time required for the fully resolved spectrum to build up as a result of the single photon creating one phonon after the other. The time-dependent spectrum also manifests the order (in time) in which the blue and red resonances (sidebands) appear in the spectrum identifying the two different mechanisms responsible for the production of these sidebands. Our study includes the coupling of the movable mirror to a mechanical heat bath. We use quantum trajectory theory combined with the input-output formalism for all calculations, but we also show how a dressed-state picture can be used to explain positions and relative strengths of all resonances. [ABSTRACT FROM AUTHOR]

In a previous paper, we pointed out the problem of missing data outside the detector range for continuous-variable entanglement verification and quantum key distribution, and we provided a straightforward solution based on entropic separability criteria (as those work better than variance-based criteria). We apply that solution here to the verification of time-frequency entanglement of photon pairs, particularly to the quantum key distribution scheme proposed by Nunn et at. [Opt. Express 21, 15959 (2013)]. We find that the scheme does lead to verifiable entanglement, but that transmission noise quickly destroys the ability to verify the entanglement [ABSTRACT FROM AUTHOR]

In continuous-variable quantum information processing, detectors are necessarily coarse grained and of finite range. We discuss how, especially, the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security when missed data outside the detector range are ignored. We demonstrate that a straightforward worst-case analysis is sufficient to avoid false positive statements about entanglement. We show that, for our worst-case analysis, entropic separability or security criteria are much superior to variance-based criteria. [ABSTRACT FROM AUTHOR]

We show how the input–output formalism for cascaded quantum systems combined with the quantum trajectory approach yields a compact and physically intuitive description of single photons propagating through a coupled cavity array. As a new application, we obtain the time-dependent spectrum of such a single photon, which directly reflects the fact that only certain frequency components of single-photon wavepackets are trapped inside the cavities and hence are delayed in time. We include in our description the actual generation of the single photon, by assuming we have a single emitter in one of the resonators.

Threshold theorems for fault-tolerant quantum computing assume that errors are of certain types. But how would one detect whether errors of the "wrong" type occur in one's experiment, especially if one does not even know what type of error to look for? The problem is that for many qubits a full state description is almost impossible to analyze due to the exponentially large state space, and a full process description requires even more resources. As a result, one simply cannot detect all types of errors. Here we show through a quantum state estimation example (on up to 25 qubits) how to attack this problem using model selection. We use, in particular, the Akaike information criterion. The example indicates that the number of measurements that one has to perform before noticing errors of the wrong type scales polynomially both with the number of qubits and with the error size. [ABSTRACT FROM AUTHOR]

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state, or (iii) only the permutationally invariant part of the density matrix is determined. We add one more method in that same spirit: We allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in the above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike information criterion. We illustrate the method by simulating experiments on (noisy) Dicke states. [ABSTRACT FROM AUTHOR]

The Hong-Ou-Mandel interference dip is caused by an entangled state, a delocalized biphoton state. We propose a method of detecting this entanglement by utilizing inverse Hong-Ou-Mandel interference, while taking into account vacuum and multiphoton contaminations, phase noise, and other imperfections. The method uses just linear optics and photodetectors, and for single-mode photodetectors we find a lower bound on the amount of entanglement. [ABSTRACT FROM AUTHOR]

We propose one and a half criteria for determining how many measurements are needed to quantify entanglement reliably. We base these criteria on Bayesian analysis of measurement results and apply our methods to four-qubit entanglement, but generalizations to more qubits are straightforward. [ABSTRACT FROM AUTHOR]

We show how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high–Qoptical cavity, by sending photons through a general, noisy channel, such as a standard optical fiber. An error correction scheme that uses few auxiliary atoms in each cavity effectively eliminates photoabsorption and other transmission errors. This realizes the ‘absorption free channel’. A concatenation protocol using the absorption free channel allows for quantum communication with single qubits over distances much larger than the coherence length of the channel.

We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. We also propose a method to correct errors during transmission.

The Casimir force in one dimension between two dielectrics with arbitrary position-dependent refractive index is calculated. A numerical procedure is developed, including renormalization and regularization, to calculate this force and the temperature correction. The force is directly derived from the electromagnetic mode structure and the corresponding eigenenergy spectrum. Some essential differences between one- and three-dimensional results are discussed.

We investigate the separation of the total angular momentum J of the electromagnetic field into a 'spin' part S and an 'orbital' part L. We show that both 'spin' and 'orbital' angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of Sz and Lz. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.

We have performed an experiment demonstrating that loop state-preparation-and-measurement tomography [Jackson and van Enk, Phys. Rev. A 92, 042312 (2015)] is capable of detecting correlated errors between the preparation and the measurement of a quantum system. Specifically, we have prepared pure and mixed states of single qubits encoded in the polarization of heralded individual photons. By performing measurements using multiple state preparations and multiple measurement device settings we are able to detect if there are any correlated errors between them, and we are also able to determine which state preparations are correlated with which measurements. This is accomplished by going around a "loop" in parameter space, which allows us to check for self-consistency. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures (POVMs) describing the detector are known. In cases where no correlations are found we are able to perform quantum state tomography of the polarization qubits by using knowledge of the detector POVMs, or quantum detector tomography by using knowledge of the state preparations. Note, however, that the detection of correlated errors does not require estimating any state or measurement parameters. [ABSTRACT FROM AUTHOR]