Ancilla States Research Articles

Efficient multi-party quantum secret-sharing protocol

ContextQuantum secret sharing allows one secret dealer to divide his/her secret among different participants. Only when all the participants pool their secret pieces together can the secret be reconstructed. Quantum secret-sharing protocol can provide high security for users who need to share some secret information among some partners. It is also a useful tool in many applications such as secure operations of joint sharing of quantum money, sharing ancilla states, and distributed quantum computation. ObjectiveWe propose a novel multi-party quantum secret-sharing protocol (MPQSSP). MethodsIn our protocol, the dealer mixes the particle sequence of the Bell states and sends the sequence to the participants. The participants encode their secret pieces into Pauli operators, which are applied to the received particle sequence. After annularly transmitting and operating the particle sequence, the participants return the particle sequence to the dealer, who can share a secret with the partners by measuring the returned sequence with the Bell basis. ResultsThe proposed MPQSSP has the merits as follows. First, its qubit efficiency can be 100% when the sample bits of the secret and the corresponding sample qubits are ignored (In our protocol when the qubit efficiency is computed, the sample bits and the corresponding Bell states used to check eavesdropping are ignored). Second, it can protect participants' privacy and interests, since the dealer cannot derive the secret piece of any participant although he/she masters the secret. Third, the participants need not perform many quantum operations and measurements to check the eavesdropping, which helps improve the efficiency of the protocol. Fourth, compared with most of the similar MPQSSPs, the quantum resources of the proposed one are relatively easier to prepare. At last, the proposed protocol has the security against various eavesdropping attacks. ConclusionThe merits above show that Our MPQSSP is relatively more practical and efficient than similar ones.

Quantum error correction with higher Gottesman-Kitaev-Preskill codes: Minimal measurements and linear optics

We propose two schemes to obtain Gottesman-Kitaev-Preskill (GKP) error syndromes by means of linear optical operations, homodyne measurements and GKP ancillae. This includes showing that for a concatenation of GKP codes with a $[n,k,d]$ stabilizer code only $2n$ measurements are needed in order to obtain the complete syndrome information, significantly reducing the number of measurements in comparison to the canonical concatenated measurement scheme and at the same time generalizing linear-optics-based syndrome detections to higher GKP codes. Furthermore, we analyze the possibility of building the required ancilla states from single-mode states and linear optics. We find that for simple GKP codes this is possible, whereas for concatenations with qubit Calderbank-Shor-Steane (CSS) codes of distance $d\geq3$ it is not. We also consider the canonical concatenated syndrome measurements and propose methods for avoiding crosstalk between ancillae. In addition, we make use of the observation that the concatenation of a GKP code with a stabilizer code forms a lattice in order to see the analog information decoding of such codes from a different perspective allowing for semi-analytic calculations of the logical error rates.

Surpassing the thermal Cramér-Rao bound with collisional thermometry

In collisional thermometry, a system in contact with the thermal bath is probed by a stream of ancillas. Coherences and collective measurements were shown to improve the Fisher information in some parameter regimes, for a stream of independent and identically prepared (i.i.d.) ancillas in some specific states [Seah et al., Phys. Rev. Lett. 123, 180602 (2019)]. Here we refine the analysis of this metrological advantage by optimizing over the possible input ancilla states, also for block-i.i.d. states of block size $b=2$. For both an indirect measurement interaction and a coherent energy exchange channel, we show when the thermal Cram\'er-Rao bound can be beaten, and when a collective measurement of $N>1$ ancilla may return advantages over single-copy measurements.

Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes

Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode k > 1 qubits in n physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually takes not only a very large resource overhead but also long in situ computation time. In this paper, we focus on Calderbank–Shor–Steane [[n, k, d]] (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitrary logical Clifford circuit can be implemented fault-tolerantly in O(1) steps in situ via either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfying k/n ∼ Θ(1), the resource scaling for Clifford circuits implementation on the logical level can be the same as on the physical level up to a constant, which is independent of code distance d. With a suitable pipeline to produce ancilla states, our scheme requires only a modest resource cost in physical qubits, physical gates, and computation time for very large scale FTQC.

Ancilla-assisted linear optical Bell measurements and their optimality

In the last decade Grice [Phys. Rev. A 84, 042331 (2011)] and Ewert and van Loock [Phys. Rev. Lett. 113, 140403 (2014)] 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 [Appl. Phys. B 72, 67 (2001)], 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 Ewert--van Loock's strategies. Furthermore, such an upper bound links the complexity of their ancilla states with the scaling of their performance. We also show a computer-aided approach to the optimization of such measurement schemes for generic interferometers, by simulating an optical network supplied with various kinds of ancillary input states. We numerically confirm the optimality of known small schemes. We use both methods to investigate other ancilla states, some of them never studied before.

Efficient preparation of large-block-code ancilla states for fault-tolerant quantum computation

Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement of a large number of clean ancilla states of different types without correlated errors inside each block. These ancilla states are usually logical stabilizer states of the data code blocks, which are generally difficult to prepare if the code size is large. Previously we have proposed an ancilla distillation protocol for Calderbank-Shor-Steane (CSS) codes by classical error-correcting codes. It was assumed that the quantum gates in the distillation circuit were perfect; however, in reality, noisy quantum gates may introduce correlated errors that are not treatable by the protocol. In this paper, we show that additional postselection by another classical error-detecting code can be applied to remove almost all correlated errors. Consequently, the revised protocol is fully fault-tolerant and capable of preparing a large set of stabilizer states sufficient for FTQC using large block codes. At the same time, the yield rate can be boosted from $O(t^{-2})$ to $O(1)$ in practice for an $[[n,k,d=2t+1]]$ CSS code. Ancilla preparation for the $[[23,1,7]]$ quantum Golay code is numerically studied in detail through Monte Carlo simulation. The results support the validity of the protocol when the gate failure rate is reasonably low. To the best of our knowledge, this approach is the first attempt to prepare general large block stabilizer states free of correlated errors for FTQC in a fault-tolerant and efficient manner.

Observation of topological Uhlmann phases with superconducting qubits

Topological insulators and superconductors at finite temperature can be characterized by the topological Uhlmann phase. However, a direct experimental measurement of this invariant has remained elusive in condensed matter systems. Here, we report a measurement of the topological Uhlmann phase for a topological insulator simulated by a system of entangled qubits in the IBM Quantum Experience platform. By making use of ancilla states, otherwise unobservable phases carrying topological information about the system become accessible, enabling the experimental determination of a complete phase diagram including environmental effects. We employ a state-independent measurement protocol which does not involve prior knowledge of the system state. The proposed measurement scheme is extensible to interacting particles and topological models with a large number of bands.

Directly Measuring the Degree of Quantum Coherence using Interference Fringes.

Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.

Decoherent histories and measurement of temporal correlation functions for Leggett-Garg inequalities

We consider two protocols for the measurement of the temporal correlation functions of a dichotomic variable $Q$ appearing in Leggett-Garg-type inequalities. The protocols measure solely whether $Q$ has the same or a different sign at the end of a given time interval, thereby measuring no more than is required for determination of the correlation function. They are inspired, in part, by a decoherent histories analysis of the two-time histories of $Q$, which yields a number of useful insights, although the protocols are ultimately expressed in macrorealistic form independent of quantum theory. The first type involves an ancilla coupled to the system with two sequential controlled-not (cnot) gates, and the two-time histories of the system (whose probabilities yield the correlation function) are determined in a single final time measurement of the ancilla. It is noninvasive for special choices of initial system states and partially invasive for more general choices. Modified Leggett-Garg-type inequalities which accommodate the partial invasiveness are discussed. The quantum picture of the protocol shows that for certain choices of the primary system initial state, the final state is unaffected by the two cnot gate interactions, hence the protocol is undetectable with respect to final system-state measurements, although it is still invasive at intermediate times. This invasiveness can be reduced with different choices of ancilla states and the protocol is then similar in flavor to a weak measurement. The second type of protocol is based on the fact that the behavior of $Q$ over a time interval can be determined from knowledge of the dynamics together with a measurement of certain initial (or final) data. Its quantum version corresponds to the known fact that when sets of histories are decoherent, their probabilities may be expressed in terms of a record projector, hence the two-time histories in which $Q$ has the same or a different sign can be determined by a single projective measurement. The resulting protocol resembles the decay-type protocol proposed by Huelga and collaborators (which is noninvasive but requires a stationarity assumption).

Improving ancilla states for quantum computation

We analyze the improvement in output state fidelity upon improving the construction accuracy of ancilla states. Specifically, we simulate gates and syndrome measurements on a single qubit of information encoded into the [[7,1,3]] quantum error correction code and determine the output state fidelity as a function of the accuracy with which Shor states (for syndrome measurements) and magic states (to implement T-gates) are constructed. When no syndrome measurements are applied during the gate sequence, we observe that the fidelity increases after performance of a T-gate and improving magic states construction slows the fidelity decay rate. In contrast, when syndrome measurements are applied, loss of fidelity occurs primarily after the syndrome measurements taken after a T-gate. Improving magic state construction slows the fidelity decay rate, and improving Shor state construction raises the initial fidelity but does not slow the fidelity decay rate. Along the way, we show that applying syndrome measurements after every gate does not maximize the output state fidelity. Rather, syndrome measurements should be applied sparingly.

Measurement-induced optical Kerr interaction

We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary interactions for continuous-variable quantum computation. Our scheme is a conceptually distinct alternative to the use of naturally occurring, weak Kerr nonlinearities or specially designed nonlinear media. Instead, we propose to exploit suitable offline prepared quartic ancilla states together with beam splitters, squeezers, and homodyne detectors. For perfect ancilla states and ideal operations, our decompositions for obtaining the measurement-based Kerr Hamiltonian lead to a realization with near-unit fidelity. Nonetheless, even by using only approximate ancilla states in the form of superposition states of up to four photons, high fidelities are still attainable. Our scheme requires four elementary operations and its deterministic implementation corresponds to about ten ancilla- based gate teleportations. We test our measurement-based Kerr interaction against an ideal Kerr Hamiltonian by applying them both to weak coherent states and single-photon superposition states.

Experimental Quantum Error Detection

Faithful transmission of quantum information is a crucial ingredient in quantum communication networks. To overcome the unavoidable decoherence in a noisy channel, to date, many efforts have been made to transmit one state by consuming large numbers of time-synchronized ancilla states. However, such huge demands of quantum resources are hard to meet with current technology and this restricts practical applications. Here we experimentally demonstrate quantum error detection, an economical approach to reliably protecting a qubit against bit-flip errors. Arbitrary unknown polarization states of single photons and entangled photons are converted into time bins deterministically via a modified Franson interferometer. Noise arising in both 10 m and 0.8 km fiber, which induces associated errors on the reference frame of time bins, is filtered when photons are detected. The demonstrated resource efficiency and state independence make this protocol a promising candidate for implementing a real-world quantum communication network.

Scalable uniform construction of highly conditional quantum gates

We present a scalable uniform technique for construction of highly conditional C$^n$-NOT quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.

A note on quantum error correction with continuous variables

We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.

Invariance of the bit error rate in the ancilla-assisted homodyne detection

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 scheme which made the bit error rate invariant.

Linear-optical implementations of the iSWAP and controlled NOT gates based on conventional detectors

The majority of linear-optical nondestructive implementations of universal quantum gates are based on single-photon resolving detectors. We propose two implementations, which are nondestructive (i.e., destroying only ancilla states) and work with conventional detectors (i.e., which do not resolve number of photons). Moreover, we analyze a recently proposed scheme of Wang et al. [J. Opt. Soc. Am. B \textbf{27}, 27 (2010)] of an optical iSWAP gate based on two ancillae in Bell's states, classical feedforward, and conventional detectors with the total probability of success equal to $\eta^4/32$, where $\eta$ is detector's efficiency. By observing that the iSWAP gate can be replaced by the controlled NOT (CNOT) gate with additional deterministic gates, we list various possible linear-optical implementations of the iSWAP gate: (i) assuming various ancilla states (unentangled, two-photon and multiphoton-entangled states) or no ancillae at all, (ii) with or without classical feedforward, (iii) destructive or nondestructive schemes, and (iv) using conventional or single-photon detectors. In particular, we show how the nondestructive iSWAP gate can be implemented with the success probability of $\eta^4/8$ assuming the same ancillae, classical feedforward, and fewer number of conventional detectors than those in the scheme of Wang {\em et al.} We discuss other schemes of the nondestructive universal gates using conventional detectors and entangled ancillae in a cluster state, Greenberger-Horne-Zeilinger and Bell's states giving the success probability of $\eta^4/4$, $\eta^6/8$, and $\eta^4/8$, respectively. In the latter scheme, we analyze how detector imperfections (dark counts in addition to finite efficiency and no photon-number resolution) and imperfect sources of ancilla states deteriorate the quantum gate operation.

Continuous-variable quantum information processing with squeezed states of light

We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.

Quantum universality by state distillation

Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This ``magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give universality, by using a simple parity-checking operation. For applications to proving threshold lower bounds, certain practical stability characteristics are often required, and we also show a stable distillation procedure.}{No distillation upper bounds are known beyond those given by the Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce to upper bounds for single-qubit ancilla states. For multi-qubit pure states and previously considered two-qubit ancilla states, the answer is yes. However, we exhibit two-qubit mixed states that are not mixtures of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. Distilling such states would require true multi-qubit state distillation methods.

Quantum universality by state distillation

Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This magic states question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give universality, by using a simple parity-checking operation. For applications to proving threshold lower bounds, certain practical stability characteristics are often required, and we also show a stable distillation procedure. No distillation upper bounds are known beyond those given by the Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce to upper bounds for single-qubit ancilla states. For multi-qubit pure states and previously considered two-qubit ancilla states, the answer is yes. However, we exhibit two-qubit mixed states that are not mixtures of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. Distilling such states would require true multi-qubit state distillation methods.

QUANTUM SECRET ENCRYPTION AND DECRYPTION IN CAVITY QED

We present a proposal of the quantum secret encryption, transmission, and decryption implementation for quantum secret-sharing protocol using cavity QED. In the proposed scheme, the information is stored in two identical two-level atoms, and the two-qubit logic transformation is realized through the interaction between atoms and a nonresonant cavity mode. The proposed scheme requires no ancilla states to assist the intermediate atomic transitions and conditional quantum dynamics for quantum phase flip and quantum state diffusion. The encryption and decryption of quantum states are mostly governed by the Hamiltonian of an atom-cavity system. Moreover, secret transmission using quasi-swap gates for entanglement swapping has also been presented. With fewer supplements of external fields, a speed quantum protocol can be realized without universal gates.