The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest failure probability. This procedure has been extended to bipartite states where the two parties, Alice and Bob, are allowed to manipulate their particles locally and communicate classically in order to determine which of two possible two-particle states they have been given. The failure probability of this local procedure has been shown to be the same as if the particles were together in the same location. Here we examine the effect of restricting the classical communication between the parties, either allowing none or eliminating the possibility that one party's measurement depends on the result of the other party's. These issues are studied for two-qubit states, and optimal procedures are found. In some cases the restrictions cause increases in the failure probability, but in other cases they do not. Applications of these procedures, in particular to secret sharing, are discussed.
We construct seven kinds of three-qubit biseparable states to show that every class of biseparable states in the partial separability classification proposed by Szalay and Kökényesi [S. Szalay and Z. Kökényesi, Phys. Rev. A 86, 032341 (2012)] is nonempty.
We consider quantum circuits with time travel designed for distinguishing specific nonorthogonal quantum states in two most popular models: Deutschs and postselected. We modify them by a presence of weakly coupled thermal environment. Using the Davies approximation we study how the thermal noise affects an ability of the circuits to distinguish nonorthogonal quantum states. We show that for purely dephasing environment a paradoxial power of such circuits remains preserved. We also present a physics based argument for conditions of validity of the maximum entropy rule introduced by David Deutsc…
Quantum non-Markovianity modifies the environmental decoherence of a system. This situation is enriched in complex systems owing to interactions among subsystems. We consider the problem of distinguishing the multiple sources of non-Markovianity using a simple power spectrum technique, applied to a qubit interacting with another qubit via a Jaynes-Cummings type Hamiltonian and simultaneously subjected to some well known noise channels, such as, the random telegraph noise and non-Markovian amplitude damping, which exhibit both Markovian as well as non-Markovian dynamics under different paramete…
We propose a protocol for Alice to implement a multiqubit quantum operation from the restricted sets on distant qubits possessed by Bob, and then we investigate the communication complexity of the task in different communication scenarios. By comparing with the previous work, our protocol works without prior sharing of entanglement, and requires less communication resources than the previous protocol in the qubit-transmission scenario. Furthermore, we generalize our protocol to $d$-dimensional operations.
Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the clas…
Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we explore the four-qubit GHZ symmetry group and its subgroup called restricted GHZ symmetry group. While the set of symmetric states under the whole group transformation is represented by three real parameters, the set of symmetric states under the subgroup transformation is represented by two real parameters. After comparing the symmetric states for whole and subgroup, the entanglement is examined for the latter set. It is shown that the set has only two SLOCC classes, $L_{abc_2}$ and $G_{abcd}$. Extension to the multi-qub…
An unknown unitary gates, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely, we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the $\frac{2}{3}π$-phase shift gate, using two discrimination schemes -- the parallel scheme and the sequential scheme. We program these two schemes on the \emph{ibmqx4}, a $5$-qubit superconducting quantum processor via IBM cloud, with the help of the $QSI$ modules [S. Liu et al.,~arXiv:1710.09500, 2…
Single-charge tunneling is a decoherence mechanism affecting superconducting qubits, yet the origin of excess quasiparticle excitations (QPs) responsible for this tunneling in superconducting devices is not fully understood. We measure the flux dependence of charge-parity (or simply, ``parity'') switching in an offset-charge-sensitive transmon qubit to identify the contributions of photon-assisted parity switching and QP generation to the overall parity-switching rate. The parity-switching rate exhibits a qubit-state-dependent peak in the flux dependence, indicating a cold distribution of exce…
The problem behind this paper is, if the number of queries to unitary operations is fixed, say $k$, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We consider the above problem for two-qubit unitary operations in the case of $k=1$, showing that for two two-qubit entangling unitary operations without local parties, LOCC achieves the same distinguishability as the global operations. Specifically, we obtain: (i) if such two unitary operations are perfectly distinguishable by global operations, then they are perfe…
In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the AC Stark effect. These unwanted photons originate from a variety of sources, such as thermal radiation, leftover measurement photons, and crosstalk. Using a capacitively-shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system…
The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, …
In this paper, we propose a protocol for complete Bell-state analysis for two superconducting-quantum-interference-device qubits. The Bell-state analysis could be completed by using a sequence of microwave pulses designed by the transition- less tracking algorithm, which is an useful method in the technique of shortcut to adiabaticity. After the whole process, the information for distinguishing four Bell states will be encoded on two auxiliary qubits, while the Bell states keep unchanged. One can read out the information by detecting the auxiliary qubits. Thus the Bell-state analysis is nondes…
While building a universal quantum computer remains challenging, devices of restricted power such as the so-called one pure qubit model have attracted considerable attention. An important step in the construction of these limited quantum computational devices is the understanding of whether the verification of the computation within these models could be also performed in the restricted scheme. Encoding via blindness (a cryptographic protocol for delegated computing) has proven successful for the verification of universal quantum computation with a restricted verifier. In this paper, we presen…
Investigations of quantum mechanical effects in macroscopic systems are of great interest to shed light onto the question where and how the transition to the classical world appears. It is also of practical relevance to determine if a bath dephasing a qubit can be described classically or requires a quantum mechanical treatment. We propose a measurement scheme to detect quantum backaction via correlation measurements to answer this question for a bath coupled to a single qubit. The presence of backaction leads to a dependence of correlations of subsequent initialization-evolution-readout cycle…
Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements
Technische Universität Wien（维也纳工业大学）；Vienna Center for Quantum Science and Technology, TU Wien（维也纳量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Department of Physics, ETH Zurich（苏黎世联邦理工学院物理系）；Quantum Center, ETH Zurich（苏黎世联邦理工学院量子中心）；Institut Quantique and Département de Physique, Université de Sherbrooke（舍布鲁克大学量子研究所及物理系）
We consider a situation in which two parties, Alice and Bob, share a 3-qubit system coupled in an initial maximally entangled, GHZ state. By manipulating locally two of the qubits, Alice can prepare any one of the eight 3-qubit GHZ states. Thus the sending of Alice's two qubits to Bob, entails 3 bits of classical information which can be recovered by Bob by means of a measurement distinguishing the eight (orthonormal) GHZ states. This contrasts with the 2-qubit case, in which Alice can prepare any of the four Bell states by acting locally only on one of the qubits.
We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investigate the topic of distinguishability of sets of quantum states in quantum communication, with particular reference to the framework of one-way local quantum operations and classical communication (LOCC). We also derive a new graph-theoretic description of distinguishability in the case of a single qubit sender.
We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of $M$ quantum channels that cannot be distinguished when one is restricted to decohered input and output states. The studied problems arise naturally in the presence of a superselection rule, allow one to quantify the amount of information that can be encoded in phase degrees of freedom (coherences), and are related to time-energy uncertainty relation. We p…
Distinguishing hot from cold is the most primitive form of thermometry. Here we consider how well this task can be performed using a single qubit to distinguish between two different temperatures of a bosonic bath. In this simple setting, we find that letting the qubit equilibrate with the bath is not optimal, and depending on the interaction time it may be advantageous for the qubit to start in a state with some quantum coherence. We also briefly consider the case that the qubit is initially entangled with a second qubit that is not put into contact with the bath, and show that entanglement a…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of 2x2 quantum states to be locally distinguishable, and for a general set of 2xn quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of ``nonlocali…
Controllable systems relying on quantum behavior to simulate distinctly quantum models so far rely on increasingly challenging classical computing to verify their results. We develop a general protocol for confirming that an arbitrary many-body system, such as a quantum simulator, can entangle distant objects. The protocol verifies that distant qubits interacting separately with the system can become mutually entangled, and therefore serves as a local test that excitations of the system can create non-local quantum correlations. We derive an inequality analogous to Bell's inequality which can …
Universal quantum computing relies on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a quantum gate, where two qubits control the operation on two target qubits (a four-qubit gate). This configuration can implement four different controlled two-qubit gates: two different entangling swap and phase operations, a phase operation distinguishing states of different parity, and the identity operation (idle quantum gate), where the choice of gate is set by the state of the control qubits. The device exploits quantum interference to control the operati…
Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in laboratories, the question of how these machine learning techniques scale with the number of qubits is becoming crucial. We empirically study the scaling of restricted Boltzmann machines (RBMs) applied to reconstruct ground-state wavefunctions of the one-dimensional transverse-field Ising model from projective measurement data. We define a learning criterion via a thres…
We consider different settings of the task to distinguish pure orthogonal quantum states under local operations and a limited amount of classical communication. In the first setting, the spatially separated parties are allowed to perform only local projective measurements without any classical communication during the measurements. Under such a restricted class of operations, if the states are indistinguishable, then within a second group of settings, the parties are allowed to use an additional resource for the distinguishing. The additional resource is either a pure entangled state or multip…
In this paper we propose a technique for distributing entanglement in architectures in which interactions between pairs of qubits are constrained to a fixed network $G$. This allows for two-qubit operations to be performed between qubits which are remote from each other in $G$, through gate teleportation. We demonstrate how adapting \emph{quantum linear network coding} to this problem of entanglement distribution in a network of qubits can be used to solve the problem of distributing Bell states and GHZ states in parallel, when bottlenecks in $G$ would otherwise force such entangled states to …
Distinguishing Ordered Phases using Machine Learning and Classical Shadows
Universidade de São Paulo（圣保罗大学）；Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；Universidade Federal de Alagoas（阿拉戈阿斯联邦大学）；Technology Innovation Institute（技术创新研究所）
Local unitary stabilizer subgroups constitute powerful invariants for distinguishing various types of multipartite entanglement. In this paper, we show how stabilizers can be used as a basis for entanglement verification protocols on distributed quantum networks using minimal resources. As an example, we develop and analyze the performance of a protocol to verify membership in the space of Werner states, that is, multi-qubit states that are invariant under the action of any 1-qubit unitary applied to all the qubits.
We consider discriminating between bipartite boxes with 2 binary inputs and 2 binary outputs (2x2) using the class of completely locality preserving operations i.e. those, which transform boxes with local hidden variable model (LHVM) into boxes with LHVM, and have this property even when tensored with identity operation. Following approach developed in entanglement theory we derive linear program which gives an upper bound on the probability of success of discrimination between different isotropic boxes. In particular we provide an upper bound on the probability of success of discrimination be…
We develop qubit Hamiltonian single parameter estimation techniques using a Bayesian approach. The algorithms considered are restricted to projective measurements in a fixed basis, and are derived under the assumption that the qubit measurement is much slower than the characteristic qubit evolution. We optimize a non-adaptive algorithm using particle swarm optimization (PSO) and compare with a previously-developed locally-optimal scheme.
Multi-spin interactions can be engineered with artificial quantum spins. However, it is challenging to verify such interactions experimentally. Here we describe two methods to characterize the $n$-local coupling of $n$ spins. First, we analyze the variation of the transition energy of the static system as a function of local spin fields. Standard measurement techniques are employed to distinguish $n$-local interactions between up to five spins from lower-order contributions in the presence of noise and spurious fields and couplings. Second, we show a detection technique that relies on time dep…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2 designs. We introduce a general method for analyzing such protocols and subsequently apply it to two subgroups, the group generated by controlled-NOT, Hadamard, and Pauli gates and that generated by only controlled-NOT and Pauli gates. In both cases the error probability can be estimated to within a factor of two or less where the factor can be arranged to b…
Numerous quantum information protocols make use of maximally entangled two-particle states, or Bell states, in which information is stored in the correlations between the two particles rather than their individual properties. Retrieving information stored in this way means distinguishing between different Bell states, yet the well known no-go theorem establishes that projective linear evolution and local measurement (LELM) detection schemes can only reliably distinguish three of the four qubit Bell states. We establish maximum distinguishability of the qutrit Bell states of bosons via projecti…
We consider tests of Leggett-Garg's macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin $1/2$ eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states (cat states). In this mapping, the unitary rotation of the Stern-Gerlach analyzer is realized by an interaction $H=Ω\hat{n}^{4}$ where $\hat{n}$ is the…
Kernel methods are used extensively in classical machine learning, especially in the field of pattern analysis. In this paper, we propose a kernel-based quantum machine learning algorithm that can be implemented on a near-term, intermediate scale quantum device. Our proposal is based on estimating classically intractable kernel functions, using a restricted quantum model known as deterministic quantum computing with one qubit. Our method provides a framework for studying the role of quantum correlations other than quantum entanglement for machine learning applications.
Matchgates are a restricted set of two-qubit gates known to be classically simulable under particular conditions. Specifically, if a circuit consists only of nearest-neighbour matchgates, an efficient classical simulation is possible if either (i) the input is a computational basis state and the simulation requires computing probabilities of multi-qubit outcomes (including also adaptive measurements), or (ii) if the input is an arbitrary product state, but the output of the circuit consists of a single qubit. In this paper we extend these results to show that matchgates are classically simulab…
We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: Whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive…
We propose two controlled remote state preparation protocols via partially entangled channels. One prepares a single-qubit state and the other prepares a two-qubit state. Different from other controlled remote state preparation schemes which also utilize partially entangled channels, neither auxiliary qubits nor two-qubit unitary transformations are required in our schemes and the success probabilities are independent of the coefficients of the quantum channel. The success probabilities are 50% and 25% for arbitrary single-qubit states and two-qubit states, respectively. We also show that the …
We propose a scheme for quantum computing using high-Q cavities in which the qubits are represented by single cavity modes restricted in the space spanned by the two lowest Fock states. We show that single qubit operations and universal multiple qubit gates can be implemented using atoms sequentially crossing the cavities.
We analyze the quantum process tomography (QPT) in the presence of decoherence, focusing on distinguishing local and non-local decoherence mechanisms for a two-partite system from experimental QPT data. In particular, we consider the $\sqrt{\rm iSWAP}$ gate realized with superconducting phase qubits and calculate the QPT matrix $χ$ in the presence of several local and non-local decoherence processes. We determine specific patterns of these decoherence processes, which can be used for a fast identification of the main decoherence mechanisms from an experimental $χ$-matrix.
Distinguishability is a fundamental and operational task generally connected to information applications. In quantum information theory, from the postulates of quantum mechanics it often has an intrinsic limitation, which then dictates and also characterises capabilities of related information tasks. In this work, we consider discrimination between bipartite two-qubit unitary transformations by local operations and classical communication (LOCC) and its relations to entangling capabilities of given unitaries. We show that a pair of entangling unitaries which do not contain local parts, if they…
Transmission of quantum states is a central task in quantum information science. Remote state preparation (RSP) has the same goal as teleportation, i.e. transferring quantum information without sending physically the information carrier, but in RSP the sender knows the state which is to be transmitted. We present experimental demonstrations of RSP for two and three locations. In our experimental scheme Alice (the preparer) and her three partners share four and six photon polarization entangled singlets. This allows us to perform RSP of two or three copies of a single qubit states, a two qubit …
The cooling effects of a nonlinear quantum oscillator via its interaction with an artificial atom (qubit) are investigated. The quantum dissipations through the environmental reservoir of the nonlinear oscillator are included, taking into account the nonlinearity of the qubit-oscillator interaction. For appropriate bath temperatures and the resonator's quality factors, we demonstrate effective cooling below the thermal background. As the photon coherence functions behave differently for even and odd photon number states, we describe a mechanism distinguishing those states. The analytical forma…
Observable-Guided Generator Selection for Improving Trainability in Quantum Machine Learning with a $ \mathfrak{g} $-Purity Interpretation under Restricted Settings
Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number of qubits. This is done by applying alternate measurements to the qubits to be distinguished. The performance of these invariants is evaluated and compared to classical invariants. We verify that the invariants can distinguish all non-isomorphic graphs with 9 or fewer nodes. The invariants have also been applied to `classically hard' strongly regular graphs,…
Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider n qubits subject to correlated Markovian dephasing and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry plays a crucial role: broken time-reversal symmetry is required for dissipative entanglement generation. Further, simply having nonzero bath susceptibilities is not enough for the dissi…
Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of Hilbert space of the system. The only information required are the number of measurements, number of outputs of each measurement and the statistics of each measurement. Earlier works on self testing restricted either to two parties scenario or multipartite graph states. Here, we construct a method to self-test the three-qubit $W$ state, and show how to extend it to other pure three-qubit states. Our …
Based on an EPR pair of qubits and allowing asymptotically secure key distribution, a secure communication protocol is presented. Bob sends either of the EPR pair qubits to Alice. Alice receives the travel qubit. Then she can encode classical information by local unitary operations on this travel qubit. Alice send the qubit back to Bob. Bob can get Alice's information by measurement on the two photons in Bell operator basis. If Eve in line, she has no access to Bob's home qubit. All her operations are restricted to the travel qubit. In order to find out which opeartion Alice performs, Eve's op…
We propose a measurement strategy which can, probabilistically, reproduce the statistics of any observable for spatially encoded photonic qubits. It comprises the implementation of a two-outcome positive operator-valued measure followed by a detection in a fixed transverse position, making the displacement of the detection system unnecessary, unlike previous methods. This strategy generalizes a scheme recently demonstrated by one of us and co-workers restricted to measurement of observables with equatorial eigenvectors only. The method presented here can be implemented with the current technol…
