We examine the stochastic dynamics of entanglement for an uncoupled two-qubit system, undergoing continuous parity measurement. Starting with a fully mixed state, the entanglement is zero for a finite amount of time, when it is suddenly created, which we refer to as entanglement genesis. There can be further entanglement sudden death/birth events culminating in the formation of a fully entangled state. We present numerical investigations of this effect together with statistics of the entanglement genesis time in the weak measurement limit as well as the quantum Zeno limit. An analytic treatment of the physics is presented, aided by the derivation of a simple concurrence equation for Bell basis X-states. The probability of entanglement border crossing and mean first passage times are calculated for the case of measurement dynamics alone. We find that states with almost the same probability of entanglement border crossing can have very different average crossing times. Our results provide insights on the optimization of entanglement generation by measurement.
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.
Producing and certifying entanglement between distant qubits is a highly desirable skill for quantum information technologies. Here we propose a new strategy to monitor and characterize entanglement genesis in a half parity measurement setup, that relies on the continuous readout of an energetic observable which is the half-parity observable itself. Based on a quantum-trajectory approach, we theoretically analyze the statistics of energetic fluctuations for a pair of continuously monitored qubits. We quantitatively relate these energetic fluctuations to the rate of entanglement produced betwee…
The stochastic evolution of quantum systems during measurement is arguably the most enigmatic feature of quantum mechanics. Measuring a quantum system typically steers it towards a classical state, destroying any initial quantum superposition and any entanglement with other quantum systems. Remarkably, the measurement of a shared property between non-interacting quantum systems can generate entanglement starting from an uncorrelated state. Of special interest in quantum computing is the parity measurement, which projects a register of quantum bits (qubits) to a state with an even or odd total …
We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Anderson's orthogonality catastrophe can be witnessed.
Semiconducting nanowires with strong Rashba spin-orbit coupling in the proximity with a superconductor and under a strong Zeeman field can potentially manifest Majorana zero modes at their edges and are a topical candidate for topological superconductivity. However, protocols for their detection based on the local and the non-local conductance spectroscopy have been subject to intense scrutiny. In this work, by taking current experimental setups into account, we detail mathematical ideas related to the entanglement entropy and the fermion parity fluctuations to faithfully distinguish between t…
We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation.
Bernstein and Varizani have given the first quantum algorithm to solve parity problem in which a strong violation of the classical imformation theoritic bound comes about. In this paper, we refine this algorithm with fewer resource and implement a two qubits algorithm in a single query on an ensemble quantum computer for the first time.
Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical performance analysis of an adaptive entanglement distillation scheme using QLDPC codes. In particular, we find that the expected yield of our adaptive distillation scheme to combat depolarization errors exceed that of Leung and Shor whenever the error probability is less than about 0.07 or greater than abou…
We present an optimal entanglement concentration ECP for an arbitrary less-entangled W state. By two of the parties say Alice and Charlie performing one parity check measurements, they can obtain the maximally entangled W state with a certain probability. Otherwise, they can obtain another lesser-entangled W state with another probability, which can be used to reconcentrated into a maximally entangled W state. By iterating this ECP several times, it has the maximal success probability. This ECP maybe an optimal one and is useful in current quantum information processing.
A multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the validity of the standard quantum theory for systems of increasing complexity, in a quasi decoherence-free environment. Because of its nonlocal structure the new system is expected to play a relevant role in the modern endeavor on quantum information and in the basic physics of entanglement.
In the presence of boundaries, the entanglement entropy in lattice models is known to exhibit oscillations with the (parity of the) length of the subsystem, which however decay to zero with increasing distance from the edge. We point out in this article that, when the subsystem starts at the boundary and ends at an impurity, oscillations of the entanglement (as well as of charge fluctuations) appear which do not decay with distance, and which exhibit universal features. We study these oscillations in detail for the case of the XX chain with one modified link (a conformal defect) or two success…
We investigate the effects of parity-deformed radiation fields on the dynamics of entanglement transfer to distant noninteracting atom qubits. These qubits are embedded in two separated lossy cavities connected by a leaky fiber, which acts as a cavity buffer with delocalized modes. The process is studied within a single-excitation subspace, the parity-deformed cavity photons allowing the introduction of static local classical fields which function as a control. The mechanism of state transfer is analyzed in comparison to the uncontrolled case. We find that the transfer evolution exhibits an as…
Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs. In spite of a high yield, the hardness of decoding a random linear code makes the use of random hashing and breeding infeasible in practice. In this pilot study, we analyze the performance of the recurrence method, a well-known entanglement distillation scheme, with its final random hashing or breeding procedure being replaced by various efficiently decodable quantum codes. Among all the replacements investigated, the one using a certain adaptive…
We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Shor-Steane (CSS) construction do not need to satisfy the dual-containing property as long as pre-shared entanglement is available to both sender and receiver. We can use this to avoid the many 4-cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product alg…
We propose a scheme for entanglement distribution among different single atoms trapped in separated cavities. In our scheme, by reflecting an input coherent optical pulse from a cavity with a single trapped atom, a controlled phase-shift gate between the atom and the coherent optical pulse is achieved. Based on this gate and homodyne detection, we construct an $n$-qubit parity gate and show its use for distribution of a large class of entangled states in one shot, including the GHZ state $\left\vert GHZ_{n}\right\rangle $, W state $\left\vert W_{n}\right\rangle $, Dicke state $\left\vert D_{n,…
We report on the realization and application of non-destructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by single-shot non-destructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the …
Protecting quantum information from errors is essential for large-scale quantum computation. Quantum error correction (QEC) encodes information in entangled states of many qubits, and performs parity measurements to identify errors without destroying the encoded information. However, traditional QEC cannot handle leakage from the qubit computational space. Leakage affects leading experimental platforms, based on trapped ions and superconducting circuits, which use effective qubits within many-level physical systems. We investigate how two-transmon entangled states evolve under repeated parity …
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the observed error syndromes. Here, we experimentally demonstrate the use of an ancillary qubit to repeatedly measure the $ZZ$ and $XX$ parity operators of two data qubits and to thereby project their joint state into the respective parity subspaces. By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the…
Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins in …
A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY) in…
This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. The proposed method produces infinitely many new codes with a wide variety of parameters and entanglement requirements. Our framework encompass…
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…
Chiral Transfer and Entanglement Generation of Even-Parity Bell States with Engineered Two-Photon Loss
School of Electronic Science and Engineering, Chongqing University of Posts and Telecommunications（重庆邮电大学电子科学与工程学院）；Chongqing Key Laboratory of Dedicated Quantum Computing and Quantum Artificial Intelligence（重庆专用量子计算与量子人工智能重点实验室）；Southwest Center for Theoretical Physics, Chongqing University（重庆大学西南理论物理中心）；Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University（重庆大学物理系及强耦合物理重庆市重点实验室）
The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyse the parity gate (P-gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with P-gates and show that native networks simplify considerably the resources required for producing multi-qubit entanglement, like n-GHZ states. Other applications include a Bell-state analyser and teleportation. We also show that cluster state fusion can be performed deterministicall…
We present a systematic entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled three-photon W state, resorting to the optical property of the quantum-dot spins inside one-sided optical microcavities. In our ECP, the parties obtain not only some three-photon systems in the partially entangled with two unknown parameters when one of the parties picks up the robust odd-parity instance with the parity-check gate (PCG) on his two photons, but also some entangled two-photon systems by keeping the even-parity instance in the first step. By exploiting the above three-photon …
We show that the computational model based on local Fermionic modes in place of qubits does not satisfy local tomography and monogamy of entanglement, and has mixed states with maximal entanglement of formation. These features directly follow from the parity conservation corresponding to the parity superselection rule. We generalize quantum superselection rules to general probabilistic theories as sets of linear constraints on the convex set of states. We then provide a link between the cardinality of the superselection rule and the degree of holism of the resulting theory.
Generating on-demand maximally entangled states is one of the corner stones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement induced dephasing processes in one of the two parity subspace. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, …
As in classical coding theory, quantum analogues of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane (CSS) construction. However, special requirements in the quantum setting severely limit the structures such quantum codes can have. While the entanglement-assisted stabilizer formalism overcomes this limitation by exploiting maximally entangled states (ebits), excessive reliance on ebits is a substantial obstacle to implementation. This paper gives necessary and sufficient conditions for the …
We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary states in a four dimensional single-particle Hilbert space, the fermion entanglement is shown to measure the entanglement between two distinguishable qubits defined by a suitable partition of this space. Such entanglement can be used as a resource for tasks like quantum teleportation. On the other hand, this fermionic entanglement provides a lower bound to t…
Measurements provide a novel mechanism for generating the entanglement resource necessary for performing scalable quantum computation. Recently, we proposed a method for performing parity measurements in a coupled quantum dot system. In this paper we generalise this scheme and perform a comprehensive analytic and numerical study of environmental factors. We calculate the effects of possible error sources including non-ideal photon detectors, ineffective spin-selective excitation and dot distinguishability (both spatial and spectral). Furthermore, we present an experimental approach for verifyi…
We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine-tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to charact…
On-demand creation of entanglement between distant qubits is a necessary ingredient for distributed quantum computation. We propose an entanglement scheme that allows for single-shot deterministic entanglement creation by detecting a single photon passing through a Mach-Zehnder interferometer with one transmon qubit in each arm. The entanglement production essentially relies on the fact that superconducting microwave structures allow to achieve strong coupling between the qubit and the photon. By detecting the photon via a photon counter, a parity measurement is implemented and the wave functi…
We present a hyperconcentration scheme for nonlocal $N$-photon hyperentangled Greenberger-Horne-Zeilinger states. The maximally hyperentangled state, in which $N$ particles are entangled simultaneously in the polarization and the spatial mode, can be obtained with a certain probability from two partially hyperentangled states. The hyperconcentration scheme is based on one polarization parity check measurement, one spatial mode parity check measurement and N-2 single-photon two-qubit measurements. The concentration only requires linear optical elements, which makes it feasible and practical wit…
We consider the Renyi alpha-entropies for Luttinger liquids (LL). For large block lengths l these are known to grow like ln l. We show that there are subleading terms that oscillate with frequency 2k_F (the Fermi wave number of the LL) and exhibit a universal power-law decay with l. The new critical exponent is equal to K/(2 alpha), where K is the LL parameter. We present numerical results for the anisotropic XXZ model and the full analytic solution for the free fermion (XX) point.
We propose coherent (`Schrödinger catlike') states adapted to the parity symmetry providing a remarkable variational description of the ground and first excited states of vibron models for finite-($N$)-size molecules. Vibron models undergo a quantum shape phase transition (from linear to bent) at a critical value $ξ_c$ of a control parameter. These trial cat states reveal a sudden increase of vibration-rotation entanglement linear ($L$) and von Neumann ($S$) entropies from zero to $L^{(N)}_{\rm cat}(ξ)\simeq 1-{2}/{\sqrt{πN}}$ [to be compared with $L^{(N)}_{\rm max.}(ξ)=1-{1}/{(N+1)}$] and $S^…
We consider the Renyi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher-Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(1/l) f…
We propose two schemes for concentration of hyperentanglement of nonlocal multipartite states which are simultaneously entangled in the polarization and spatial modes. One scheme uses an auxiliary singlephoton state prepared according to the parameters of the less-entangled states. The other scheme uses two less-entangled states with unknown parameters to distill the maximal hyperentanglement. The procrustean concentration is realized by two parity check measurements in both the two degrees of freedom. Nondestructive quantum nondemolition detectors based on cross-Kerr nonlinearity are used to …
Recent work has shown that use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and p…
We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through $XYZ$ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the r…
Quantum error correction requires the detection of errors by reliable measurements of suitable multi-qubit correlation operators. Here, we experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. An additional 'flag' qubit serves to detect errors occurring throughout the parity measurement, which would otherwise proliferate into uncorrectable weight-2 errors on the qubit register. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)\%. Deliberately injecting bit and phase-flip errors, we show that the fault-tolerant protocol is capable o…
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that due to the parity conserving nature of the coupling, the asymptotic entanglement is considerably…
While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with $49\%$ concurrence and $73\%$ Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly-identical transmon-resonator systems. By ensuring the measured output field does not distinguish $\vert 01 \rangle$ from $\vert 10 \rangle$, unentangled superposition states are probabili…
The measurement of the parity of two qubits is a primitive of quantum computing that allows creating deterministic entanglement. In the field of circuit quantum electrodynamics, a scheme to achieve parity measurement of two superconducting qubits has been proposed and analyzed under the usual rotating-wave approximation (RWA). We show that the same scheme can be carried over beyond this approximation, to the regime of ultrastrong coupling, with an improvement in the fidelity.
We study Bell inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on/off measurements and photon number parity measurements, respectively, are investigated. When photon on/off measurements are used, at least 50% of detec- tion efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son…
