Complete and precise characterization of a quantum dynamical process can be achieved via the method of quantum process tomography. Using a source of correlated photons, we have implemented several methods investigating a wide range of processes, e.g., unitary, decohering, and polarizing. One of these methods, ancilla-assisted process tomography (AAPT), makes use of an additional ``ancilla system,'' and we have theoretically determined the conditions when AAPT is possible. All prior schemes for AAPT make use of entangled states. Our results show that, surprisingly, entanglement is not required for AAPT, and we present process tomography data obtained using an input state that has no entanglement. However, the use of entanglement yields superior results.
We show that how a recent experiment of quantum imaging with undetected photons can basically be described as a (partial) ancilla-assisted process tomography. We propose a simplified quantum circuit version of this scenario, which also enables to recast quantum imaging in quantum computation language. Our analogy and analysis may help better understand the role of classical and/or quantum correlations in imaging experiments.
Standard quantum process tomography on a $d$-dimensional input is performed by preparing several states of an input probe that then evolve under the action of the quantum channel corresponding to the progress. The final states of the probe are reconstructed by means of state tomography. An alternative is offered by ancilla-assisted process tomography: a single probe-ancilla state is used, and the correlations existing between probe and ancilla are exploited to fully reconstruct the information on the channel. In order for ancilla-assisted process tomography to be possible, the probe-ancilla in…
The standard method of Quantum State Tomography (QST) relies on the measurement of a set of noncommuting observables, realized in a series of independent experiments. Ancilla Assisted QST (AAQST) proposed by Nieuwenhuizen and co-workers (Phys. Rev. Lett., 92, 120402 (2004)) greatly reduces the number of independent measurements by exploiting an ancilla register in a known initial state. In suitable conditions AAQST allows mapping out density matrix of an input register in a single experiment. Here we describe methods for explicit construction of AAQST experiments in multi-qubit registers. We a…
Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present the theory describing a new type of method for quantum process tomography. We describe an algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two main virtues: it requires investing a number of physical resources scaling polynomially with the…
We propose and demonstrate a novel method to generate a large-amplitude coherent-state superposition (CSS) via ancilla-assisted photon-subtraction. The ancillary mode induces quantum interference of indistinguishable processes, widening the controllability of quantum superposition at the conditional output. We demonstrate the concept in the time domain, by a simple time-separated two-photon subtraction from cw squeezed light. We observe the largest CSS ever reported without any corrections, which will enable various quantum information applications with CSS states.
The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated …
We study interferometry with Gaussian states and show that an ancilla-assisted scheme outperforms coherent state interferometry for all levels of loss. We also compare the ancilla-assisted scheme to other interferometric schemes involving squeezing, and show that it is the most advantage in the high-loss, high photon-number regime. In fact, in the presence of high loss, it out-performs many other strategies proposed to date. We find the optimal measurement observable for each scheme discussed. We also find that with the appropriate measurement, the achievable precision of the proposal by Caves…
It is well known that one can extract all the information of an unknown quantum channel by means of quantum process tomography, such as standard quantum-process tomography and ancilla-assisted quantum process tomography (AAQPT). Furthermore, it has been shown that entanglement is not necessary for AAQPT, there exist separable states which are also useful for it. Surprisingly, in this work we find that not all entangled states are useful for AAQPT, there also exist some entangled states which are useless. The realignment operation used in entanglement detection can be related to the question wh…
A system-ancilla bipartite state capable of containing the complete information of an unknown quantum channel acting on the system is called faithful. The equivalence between faithfulness of state and invertibility of the corresponding Jamiolkowski map proved by D'Ariano and Presti has been a useful characterization for ancilla-assisted process tomography albeit the proof was incomplete as they assumed trace nonincreasing quantum operations, not quantum channels. We complete the proof of the equivalence and introduce the generalization of faithfulness to various classes of quantum channels. We…
We show that weighted unitary 2-designs define optimal measurements on the system-ancilla output state for ancilla-assisted process tomography of unital quantum channels. Examples include complete sets of mutually unbiased unitary-operator bases. Each of these specifies a minimal series of optimal orthogonal measurements. General quantum channels are also considered.
In order to make a unified treatment for estimation problems of a very small noise or a very weak signal in a quantum process, we introduce the notion of a low-noise quantum channel with one noise parameter. It is known in several examples that prior entanglement together with nonlocal output measurement improves the performance of the channel estimation. In this paper, we study this ``ancilla-assisted enhancement'' for estimation of the noise parameter in a general low-noise channel. For channels on two level systems we prove that the enhancement factor, the ratio of the Fisher information of…
We report an experiment in which the moments of spatial coordinates of down-converted photons are measured directly, without having to reconstruct any marginal probability distributions. We use a spatial light modulator to couple the spatial degrees of freedom and the polarization of the fields, which act as ancilla systems. Information about the spatial correlations is obtained via measurements on the ancilla qubits. Among other applications, this new method provides a more efficient technique to identify continuous variable entanglement.
We investigated the minimum achievable bit error rate of discriminating binary coherent states by homodyne measurements with the help of arbitrary ancilla states coupled via beam splitters. We took into account arbitrary pure ancillary states those were updated in real-time by those partial measurements and classical feedforward operations where the partial measurements were made by homodyne detections with a common fixed phase. It was shown that the minimum bit error rate of the system was invariant under these operations. We also discussed how generalize the homodyne detection beyond the sch…
Quantum ensembles form easily accessible architectures for studying various phenomena in quantum physics, quantum information science, and spectroscopy. Here we review some recent protocols for measurements in quantum ensembles by utilizing ancillary systems. We also illustrate these protocols experimentally via nuclear magnetic resonance techniques. In particular, we shall review noninvasive measurements, extracting expectation values of various operators, characterizations of quantum states, and quantum processes, and finally quantum noise engineering.
It has been demonstrated that the optimal sensitivity achievable with Greenberger-Horne-Zeilinger states is the same as that with uncorrelated probes in the frequency estimation in the presence of uncorrelated Markovian dephasing [S. F. Huelga, et al., Phys. Rev. Lett. 79, 3865 (1997)]. Here, we extend this issue by examining the optimal frequency sensitivities achievable by the use of ancilla-assisted strategy, which has been proposed recently for robust phase estimation. We present the ultimate frequency sensitivities bounded by the quantum Fisher information for a general case in the presen…
The standard procedure for quantum process tomography (QPT) involves applying the quantum process on a system initialized in each of a complete set of orthonormal states. The corresponding outputs are then characterized by quantum state tomography (QST), which itself requires the measurement of non-commuting observables realized by independent experiments on identically prepared system states. Thus QPT procedure demands a number of independent measurements, and moreover, this number increases rapidly with the size of the system. However, the total number of independent measurements can be grea…
In the last decade Grice and Ewert and van Loock found linear optical networks achieving near-unit efficiency unambiguous Bell state discrimination, when fed with increasingly complex ancillary states. However, except for the vacuum ancilla case, the optimality of these schemes is unknown. Here, the optimality of these networks is investigated through analytical and numerical means. We show an analytical upper bound to the success probability for interferometers that preserve the polarization of the input photons, saturated by both Grice's and Evert-van Loock's strategies. Furthermore, such an…
The metrological ability of carefully designed probes can be spoilt by the presence of noisy processes occurring during their evolution. The noise is responsible for altering the evolution of the probes in such a way that bear little or no information on the parameter of interest, hence spoiling the signal-to-noise ratio of any possible measurement. Here we show an experiment in which the introduction of an ancilla improves the estimation of an optical phase in the high-noise regime. The advantage is realised by the coherent coupling of the probe and the ancilla at the initialisation and the m…
Work is an observable quantity associated with a process, however there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von-Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality an…
While a bit is the fundamental unit of binary classical information, a qubit is the fundamental unit of quantum information. In quantum information processing (QIP), it is customary to call the qubits under study as system qubits, and the additional qubits as ancillary qubits. In this thesis, I describe various schemes to exploit the ancillary qubits to efficiently perform many QIP tasks and their experimental demonstrations in nuclear magnetic resonance (NMR) systems. Particularly, we have showed that, in the presence of sufficient ancillary qubits, it is possible to completely characterize a…
A quantum measurement can be described by a set of matrices, one for each possible outcome, which represents the positive operator-valued measure (POVM) of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are required. We present the first experimental POVM reconstruction that takes explicit advantage of a quantum resource, i.e., nonclassical correlations with an ancillary state. A POVM of a photon-number-resolving detector is reconstructed by using strong quantum correlations of twin beams generated by parametric down-conversion. Our reconstruction method is more stati…
We report the experimental demonstration of a transmission scheme of photonic qubits over unstabilized optical fibers, which has the plug-and-play feature as well as the ability to transmit any state of a qubit, regardless of whether it is known, unknown, or entangled to other systems. A high fidelity to the noiseless quantum channel was achieved by adding an ancilla photon after the signal photon within the correlation time of the fiber noise and by performing quantum parity checking. Simplicity, maintenance-free feature and robustness against path-length mismatches among the nodes make our s…
A scheme for improving the sensitivity of quantum thermometry is proposed where the sensing quantum system used to recover the temperature of an external bath is dynamically coupled with an external ancilla (a meter) via a Hamiltonian term $\hat{H}_I$. At variance with previous approaches, our scheme relies neither on the presence of initial entanglement between the sensor and the meter, nor on the possibility of performing joint measurements on the two systems. The advantages we report arise from the fact that the presence of $\hat{H}_I$ interferes with the bath-sensor interaction, transformi…
We show here through experiments and exact analytical models the emergence of discrete time translation symmetry breaking in non-interacting systems. These time-periodic structures become stable against perturbations only in the presence of their interaction with the ancillary quantum system and display subharmonic response over a range of rotation angle errors. We demonstrate this effect for central spin and spin-mechanical systems, where the ancillary induced interaction among the spins stabilizes the spin dynamics against finite errors. Further, we extend these studies and show the possibil…
We show that for some noisy channels, the optimal entanglement-assisted strategy depends on the noise level. We note that there is a non-trivial crossover between the parallel-entangled strategy and the ancilla-assisted strategy - in the former the probes are all entangled, the latter the probes are entangled with a noiseless ancilla but not amongst themselves. The transition can be explained by the fact that, separable states are more robust against noise and therefore are optimal in the high noise limit, but they are in turn outperformed by ancilla-assisted ones.
Neural networks (NNs) representing quantum states are typically trained using Markov chain Monte Carlo based methods. However, unless specifically designed, such samplers only consist of local moves, making the slow-mixing problem prominent even for extremely simple quantum states. Here, we propose to use mode-assisted training that provides global information via the modes of the NN distribution. Applied to quantum state tomography using restricted Boltzmann machines, this method improves the quality of reconstructed quantum states by orders of magnitude. The method is applicable to other typ…
Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, which limits the performance of such ancilla-assisted quantum control. To address this challenge of ancilla-induced decoherence, we propose a general framework that integrates quantum control and quantum error correction, so that we can achieve robust quantum gates resilient to ancilla noise. We introduce the path independence criterion for fault-tolerant quantum gates against ancilla errors. As an example, a path-indep…
Entanglement-assisted quantum communication employs pre-shared entanglement between sender and receiver as a resource. We apply the same framework to quantum metrology, introducing shared entanglement between the preparation and the measurement stage, namely using some entangled ancillary system that does not interact with the system to be sampled. This is known to be useless in the noiseless case, but was recently shown to be useful in the presence of noise. Here we detail how and when it can be of use. For example, surprisingly it is useful when randomly time sharing two channels where ancil…
We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's pre-shared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a "witness". Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the send…
We study the efficiency of quantum tomographic reconstruction where the system under investigation (quantum target) is indirectly monitored by looking at the state of a quantum probe that has been scattered off the target. In particular we focus on the state tomography of a qubit through a one-dimensional scattering of a probe qubit, with a Heisenberg-type interaction. Via direct evaluation of the associated quantum Cramér-Rao bounds, we compare the accuracy efficiency that one can get by adopting entanglement-assisted strategies with that achievable when entanglement resources are not availab…
When measuring quantum spins at two or more different times, the later measurements are affected by measurement backaction occurring due to the earlier measurements. This makes the measurement of temporal quantum correlation functions challenging. In this paper, I propose a measurement protocol that mitigates the effect of measurement backaction by exploiting spin selection rules. I show that, under suitable conditions, the effect of measurement backaction on two-time quantum correlations becomes negligible when probing a system consisting of spins with large spin quantum numbers $l\gg s$ by c…
Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value requires a low postselection probability for an ancilla degree of freedom, which limits the utility of the technique. We propose an improvement to this method that uses entanglement to increase the efficiency. We show that by entangling and postselecting $n$ ancillas, the postselection probability can be increased by a factor of $n$ while keeping the weak…
We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the "no-go" theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary …
We propose a nonlocal entanglement concentration protocol (ECP) for $N$-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an $N$-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state and it is the resource in the next round of entanglement conce…
We argue that the claimed optimality of a new process tomography method suggested in [quant-ph/0601033] and [quant-ph/0601034] is based on not completely fair comparison that does not take into account the available information in an equal way. We also argue that the method is not a new process tomography scheme, but rather represents an interesting modification of ancilla assisted process tomography method. In our opinion these modifications require deeper understanding and further investigation.
Quantum tomography is an important tool for the characterisation of quantum operations. In this paper, we present a framework of quantum tomography in fermionic systems. Compared with qubit systems, fermions obey the superselection rule, which sets constraints on states, processes and measurements in a fermionic system. As a result, we can only partly reconstruct an operation that acts on a subset of fermion modes, and the full reconstruction always requires at least one ancillary fermion mode in addition to the subset. We also report a protocol for the full reconstruction based on gates in Ma…
We review the use of an external auxiliary detector for measuring the full distribution of the work performed on or extracted from a quantum system during a unitary thermodynamic process. We first illustrate two paradigmatic schemes that allow one to measure the work distribution: a Ramsey technique to measure the characteristic function and a positive operator valued measure (POVM) scheme to directly measure the work probability distribution. Then, we show that these two ideas can be understood in a unified framework for assessing work fluctuations through a generic quantum detector and descr…
Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement…
We present an indirect two-qubit parity meter in planar circuit quantum electrodynamics, realized by discrete interaction with an ancilla and a subsequent projective ancilla measurement with a dedicated, dispersively coupled resonator. Quantum process tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum non-demolition. Separate interaction and measurement steps allow commencing subsequent data qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.
Given a quantum state with an unknown parameter, the Quantum Fisher Information (QFI) is a measure of the amount of information that an observable can extract about the parameter. QFI also quantifies the maximum achievable precision in estimating the parameter with a given amount of resource via an inequality known as quantum Cramer-Rao bound. In this work, we describe a protocol to amplify QFI of a single target qubit precorrelated with a set of ancillary qubits. A single quadrature measurement of only ancillary qubits suffices to perform the complete quantum state tomography (QST) of the tar…
