The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We generalize this to a large four-parameter family of qubit channels and for the average fidelity over all pure states. As a by-product we classify all the qubit channels which have one invariant pure state and show that the parameter manifold of these channels is isomorphic to $S^2\times S^1\times S^1$ and contains many interesting subclasses of channels. The figure of merit that we use is the average input-output fidelity which we show can be increased up to $30$ percents in some cases, by tuning of the weak measurement parameter.
We consider novel implementation of quantum teleportation protocol of unknown qubit with entangled hybrid state. Coherent components of the entangled hybrid state displace the teleported qubit at the same absolute but opposite in sign values, so that any information about amount by which the qubit is displaced is lost despite the fact that one of these events has definitely occurred. Alice unambiguously distinguishes her measurement outcomes and Bob obtains at his disposal states of a single photon in superposition of two modes with controllable amplitude distortions. We consider the implement…
We propose a scheme for both distilling and quantifying entanglement, applicable to individual copies of an arbitrary unknown two-qubit state. It is realized in a usual two-qubit interferometry with local filtering. Proper filtering operation for the maximal distillation of the state is achieved, by erasing single-qubit interference, and then the concurrence of the state is determined directly from the visibilities of two-qubit interference. We compare the scheme with full state tomography.
We discuss a state discriminator that unambiguously distinguishes between two quantum registers prepared with multiple copies of two unknown qubits. This device achieves the optimal performance by von Neumann measurement and general POVM in different ranges of the input preparation probabilities, respectively, and in the limit of very large program registers the optimal measurement reduces to only von Neumann measurements.
By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits [An Min Wang: PRA, \textbf{74}, 032317(2006)], we present a scheme to implement it in cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction between the atoms and the field of cavity is a nonresonant one. Finally, we analyze the experimental feasibility of this scheme.
Suppose, we are given two finite ensembles of pure qubit states, so that the qubits in each ensemble are prepared in identical (but unknown for us) states lying on the equator of the Bloch sphere. What is the best strategy to estimate fidelity between these two finite ensembles of qubit states? We discuss three possible strategies for the fidelity estimation. We show that the best strategy includes two stages: a specific unitary transformation on two ensembles and state estimation of the output states of this transformation.
Acquiring information about an unknown qubit in a superposition of two states is essential in any computation process. Quantum measurement, or sharp measurement, is usually used to read the information contents of that unknown qubit system. Quantum measurement is an irreversible operation that makes the superposition collapses to one of the two possible states in a probabilistic way. In this paper, a quantum algorithm will be proposed to read the information in an unknown qubit without applying sharp measurement on that qubit. The proposed algorithm will use a quantum feedback control scheme b…
We propose an experimental setup that is capable of unambiguously discriminating any pair of linearly independent single photon polarization qubits, about which we don't have any knowledge except that an extra pair of these unknown states are provided as the reference. This setup, which is constructed with optical CNOT gates, weak cross Kerr non-linearities, Bell state analysers and other linear optical elements, transforms the unknown triple photon input states to the corresponding single photon states to be deterministically processed by linear optics circuit. The optimal discrimination of t…
Consider an n qubit computational basis state corresponding to a bit string x, which has had an unknown local unitary applied to each qubit, and whose qubits have been reordered by an unknown permutation. We show that, given such a state with Hamming weight |x| at most n/2, it is possible to reconstruct |x| with success probability 1 - |x|/(n-|x|+1), and thus to compute any symmetric function of x. We give explicit algorithms for computing whether or not |x| is at least t for some t, and for computing the parity of x, and show that these are essentially optimal. These results can be seen as ge…
We propose and develop theory of quantum teleportation of unknown qubit based on interaction mechanism between discrete-variable (DV) and continuous-variable (CV) states on highly transmissive beam splitter (HTBS). This DV-CV interaction mechanism is based on simultaneous displacement of the discrete-variable state on equal in absolute value but opposite in sign displacement amplitudes by coherent components of the hybrid, in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary modes
Quantum teleportation circumvents the uncertainty principle using dual channels: a quantum one consisting of previously-shared entanglement, and a classical one, together allowing the disembodied transport of an unknown quantum state over distance. It has recently been shown that a classical bit can be counterfactually communicated between two parties in empty space, "Alice" and "Bob". Here, by using our "dual" version of the chained quantum Zeno effect to achieve a counterfactual CNOT gate, we propose the first protocol for transporting an unknown qubit counterfactually, that is without any p…
We present a way of directly manipulating an arbitrary qubit, without the exchange of any particles. This includes as an application the exchange-free preparation of an arbitrary quantum state at Alice by a remote classical Bob. As a result, we are able to propose a protocol that allows one party to directly enact, by means of a suitable program, any computation exchange-free on a remote second party's unknown qubit. Further, we show how to use this for the exchange-free control of a universal two-qubit gate, thus opening the possibility of directly enacting any desired algorithm remotely on a…
We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used. Nonlinear effect on the teleported state is realized due to peculiarity of interaction of coherent components with discrete variable state on a beam splitter. Bob performs unitary transformation after receiving the appropriate classical information. The protocol is nearly deterministic but the output state is subject to amplitude distortion which reduces the fid…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown n-qubit pair-interaction Hamiltonian into a conditional one such that standard phase estimation can be applied to measure the energy. Our essential assumption is that the considered system can be brought into interaction with a quantum computer. For large n the algorithm could still be applicable for estimating the density of energy states and might therefore b…
In projective measurements of energy, a target system is projected to an eigenstate of the system Hamiltonian, and the measurement outcomes provide the information of corresponding eigen-energies. Recently, it has been shown that such a measurement can be in principle realized without detailed knowledge of the Hamiltonian by using probe qubits. However, in the previous approach for the energy measurement, the necessary size of the dimension for the probe increases as we increase the dimension of the target system, and also individual addresibility of every qubit is required, which may not be p…
We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean-square errors when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative Cramer-Rao bound and Hayashi-Gill-Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given $n$ quantum states t…
Self testing is a device independent approach to estimate the state and measurement operators, without the need to assume the dimension of our quantum system. In this paper, we show that one can self test black boxes into any pure entangled two-qubit state, by performing simple Bell type experiments. The approach makes use of only one family of two-inputs/two-outputs Bell inequalities. Furthermore, we outline the sufficient conditions for one to self test any dimensional bipartite entangled state. All these methods are robust to small but inevitable experimental errors.
We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and Haah 3D code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phase-flip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for t…
It is not possible to disentangle a qubit in an unknown state $|ψ>$ from a set of (N-1) ancilla qubits prepared in a specific reference state $|0>$. That is, it is not possible to {\em perfectly} perform the transformation $(|ψ,0...,0\r +|0,ψ,...,0\r +...+ |0,0,...ψ\r) \to |0,...,0>\otimes |ψ>$. The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in an known state. Measuring the whole system is, as expected, the least effective method. We present various quan…
Whether entanglement in a state can be detected, distilled, and quantified without full state reconstruction is a fundamental open problem. We demonstrate a new scheme encompassing these three tasks for arbitrary two-qubit entanglement, by constructing the optimal entanglement witness for polarization-entangled mixed-state photon pairs without full state reconstruction. With better efficiency than quantum state tomography, the entanglement is maximally distilled by newly developed tunable polarization filters, and quantified by the expectation value of the witness, which equals the concurrence…
The probability of successfully controlled teleportating an unknown qubit using a general three-particle state is investigated. We give the analytic expressions of maximal probabilities of successfully controlled teleportating an unknown qubit via several kinds of tripartite states including a tripartite GHZ state and a tripartite W-state.
Undoing a unitary operation, $i.e$. reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any specific description, however, it is a hard and challenging task to realize the inverse operation. Recently, a universal quantum circuit has been proposed [Phys.Rev.Lett. 123, 210502 (2019)] to undo an arbitrary unknown $d$-dimensional unitary $U$ by implementing its inverse with a certain probability. In this letter, we report the experimental reversing of three …
We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a non-local property, optimally.
We present a physical scheme for entanglement concentration of unknown atomic entangled states via cavity decay. In the scheme, the atomic state is used as stationary qubit and photonic state as flying qubit, and a close maximally entangled state can be obtained from pairs of partially entangled states probabilistically.
A quantum analog of the fundamental classical NOT gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking phenomenon has far-reaching implications concerning quantum information processing and encoding information about directions and reference frames into quantum states. It also triggers the question under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalizati…
The implementation of polarization-based quantum communication is limited by signal loss and decoherence caused by the birefringence of a single-mode fiber. We investigate the Knill dynamical decoupling scheme, implemented using half-wave plates, to minimize decoherence and show that a fidelity greater than $99\%$ can be achieved in absence of rotation error and fidelity greater than $96\%$ can be achieved in presence of rotation error. Such a scheme can be used to preserve any quantum state with high fidelity and has potential application for constructing all optical quantum delay line, quant…
We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal superposition of the original and its complement state. Surprisingly, we find that Hadamard transformations exist for an unknown qubit chosen either from the polar or equatorial great circles. Also, we show that for an unknown qubit one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement state. We dis…
We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters -- explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling …
We experimentally demonstrate in NMR a quantum interferometric multi-meter for extracting certain properties of unknown quantum states without resource to quantum tomography. It can perform direct state determinations, eigenvalue/eigenvector estimations, purity tests of a quantum system, as well as the overlap of any two unknown quantum states. Using the same device, we also demonstrate one-qubit quantum fingerprinting.
We consider several problems that involve finding the eigenvalues and generating the eigenstates of unknown unitary gates. We first examine Controlled-U gates that act on qubits, and assume that we know the eigenvalues. It is then shown how to use singlet states to produce qubits in the eigenstates of the gate. We then remove the assumption that we know the eigenvalues and show how to both find the eigenvalues and produce qubits in the eigenstates. Finally, we look at the case where the unitary operator acts on qutrits and has eigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerat…
Quantum gates (unitary gates) on physical systems are usually implemented by controlling the Hamiltonian dynamics. When full descriptions of the Hamiltonians parameters is available, the set of implementable quantum gates is easily characterised by quantum control theory. In many real systems, however, the Hamiltonians may include unknown parameters due to the difficulty of precise measurements or instability of the system. In this paper, we consider the situation that some parameters of the Hamiltonian are unknown, but we still want to perform a robust control of a quantum gate irrespectively…
Recently quantum states discrimination has been frequently studied. In this paper we study them from the other way round, the likeness of two quantum states. The fidelity is used to describe the likeness of two quantum states. Then we presented a scheme to obtain the fidelity of two unknown qubits directly from the integral area of the spectra of the assistant qubit(spin) on an NMR Quantum Information Processor. Finally we demonstrated the scheme on a three-qubit quantum information processor. The experimental data are consistent with the theoretical expectation with an average error of 0.05, …
We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one-particle and two-particle and construct efficient quantum logic networks for implementing the new schemes by means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations. In these schemes the teleportation are not always successful but with certain probability.
Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver's state has more quantum discord than the sender's state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob's qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting fea…
We give the analytic expressions of maximal probabilities of successfully controlled teleportating an unknown qubit via every kind of tripartite states. Besides, another kind of localizable entanglement is also determined. Furthermore, we give the sufficient and necessary condition that a three-qubit state can be collapsed to an EPR pair by a measurement on one qubit, and characterize the three-qubit states that can be used as quantum channel for controlled teleporting a qubit of unknown information with unit probability and with unit fidelity.
We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors in terms of the lowest value (i.e., equal to 1) of a condition number, as required by the Gastinel-Kahan theorem. In contrast, standard tomographic protocols, including those based on mutually unbiased bases, are nonoptimal for determining all 16 elements of an unknown two-qubit density matrix. Our method is based on the measurements of the 16 generalized P…
Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA state, local operation and classical communication we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined with a post-selection scheme conditioned on the measurement result obtained on one of the qubits of the pair. The resulting transformation is a deterministic, nonlinear, chaotic map in the Hilbert space. We derive a class of these transformations capable of orthogonalizing nonorthogonal qubit states after a few iterations. These nonlinear maps orthogonalize st…
We prove a new impossibility for quantum information (the no-splitting theorem): an unknown quantum bit (qubit) cannot be split into two complementary qubits. This impossibility, together with the no-cloning theorem, demonstrates that an unknown qubit state is a single entity, which cannot be cloned or split. This sheds new light on quantum computation and quantum information.
In this paper, we consider the problem of open-loop control of a qubit that is coupled to an unknown fully quantum non-Markovian noise (either bosonic or fermionic). A graybox model that is empirically obtained from measurement data is employed to approximately represent the unknown quantum noise. The estimated model is then used to calculate the open-loop control pulses under constraints on the pulse amplitude and timing. For the control pulse optimization, we explore the use of gradient descent and genetic optimization methods. We consider the effect of finite sampling on estimating expectat…
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal collective entanglement witness detecting all two-qubit entanglement. The test is directly linked to a function which characterizes to some extent the entanglement quantitatively. This function is an entanglement monotone under so--called local pure operations and classical communication (pLOCC) which preserve local dimensions. Moreover it provides tight up…
For an unknown eigenstate $|ψ\rangle$ of a unitary operator $U$, suppose we have an estimate of the corresponding eigenvalue which is separated from all other eigenvalues by a minimum gap of magnitude $Δ$. In the eigenstate-marking problem (EMP), the goal is to implement a selective phase transformation of the $|ψ\rangle$ state (known as \emph{marking} the $|ψ\rangle$ state in the language of the quantum search algorithms). The EMP finds important applications in the construction of several quantum algorithms. The best known algorithm for the EMP combines the ideas of the phase estimation algo…
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, …
We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can be measured directly on equal footing with the real part of the weak value. We present compact expressions for the weak value of single qubit observables and of product observables on qubit pairs. Experimental studies of the results are suggested with cold trapped ions.
Quantum process tomography has become increasingly critical as the need grows for robust verification and validation of candidate quantum processors. Here, we present an approach for efficient quantum process tomography that uses a physically motivated ansatz for an unknown quantum process. Our ansatz bootstraps to an effective description for an unknown process on a multi-qubit processor from pairwise two-qubit tomographic data. Further, our approach can inherit insensitivity to system preparation and measurement error from the two-qubit tomography scheme. We benchmark our approach using nume…
Quantum sensors may provide extremely high sensitivity and precision to extract key information in a quantum or classical physical system. A fundamental question is whether a quantum sensor is capable of uniquely inferring unknown parameters in a system for a given structure of the quantum sensor and admissible measurement on the sensor. In this paper, we investigate the capability of a class of quantum sensors which consist of either a single qubit or two qubits. A quantum sensor is coupled to a spin chain system to extract information of unknown parameters in the system. With given initialis…
We analyze quantum state estimation for finite samples based on symmetry information. The used measurement concept compares an unknown qubit to a reference state. We describe explicitly an adaptive strategy, that enhances the estimation fidelity of these measurements.
We study the dynamics of a Heisenberg-XY spin chain with an unknown state coded into one qubit or a pair of entangled qubits, with the rest of the spins being in a polarized state. The time evolution involves magnon excitations, and through them the entanglement is transported across the channel. For a large number of qubits, explicit formulae for the concurrences, measures for two-qubit entanglements, and the fidelity for recovering the state some distance away are calculated as functions of time. Initial states with an entangled pair of qubits show better fidelity, which takes its first maxi…
An experiment is performed to reconstruct an unknown photonic quantum state with a limited amount of copies. A semi-quantum reinforcement learning approach is employed to adapt one qubit state, an "agent," to an unknown quantum state, an "environment," by successive single-shot measurements and feedback, in order to achieve maximum overlap. The experimental learning device herein, composed of a quantum photonics setup, can adjust the corresponding parameters to rotate the agent system based on the measurement outcomes "0" or "1" in the environment (i.e., reward/punishment signals). The results…
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments. Monitoring rapid qubit dynamics, e.g. during quantum gates, requires more complicated methods with increased demand for prior information. Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a Lo…
Future quantum technologies rely heavily on good protection of quantum entanglement against environment-induced decoherence. A recent study showed that an extension of Uhrig's dynamical decoupling (UDD) sequence can (in theory) lock an arbitrary but known two-qubit entangled state to the $N$th order using a sequence of $N$ control pulses [Mukhtar et al., Phys. Rev. A 81, 012331 (2010)]. By nesting three layers of explicitly constructed UDD sequences, here we first consider the protection of unknown two-qubit states as superposition of two known basis states, without making assumptions of the s…
We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that contrary to the impossibility of perfect quantum cloning, the quantum-phase can be synchronized perfectly through a joined unitary operation. When both qubits are initially in a pure unknown state, perfect quantum-phase synchronization through unitary operations becomes impossible. In this situation we determine the maximum average quantum-phase synchronization fidelity, the distribution o…
We demonstrate the conditional reversal of a weak (partial-collapse) quantum measurement on a photonic qubit. The weak quantum measurement causes a nonunitary transformation of a qubit which is subsequently reversed to the original state after a successful reversing operation. Both the weak measurement and the reversal operation are implemented linear optically. The state recovery fidelity, determined by quantum process tomography, is shown to be over 94% for partial-collapse strength up to 0.9. We also experimentally study information gain due to the weak measurement and discuss the role of t…
In recent decades, a great variety of researches and applications concerning Bell nonlocality have been developed with the advent of quantum information science. Providing that Bell nonlocality can be revealed by the violation of a family of Bell inequalities, finding maximal Bell violation (MBV) for unknown quantum states becomes an important and inevitable task during Bell experiments. In this paper we introduce a self-guide method to find MBVs for unknown states using a stochastic gradient ascent algorithm (SGA), by parameterizing the corresponding Bell operators. For all the investigated s…
In distributed quantum information processing, flying photons entangle matter qubits confined in cavities. However, when a matter qubit is homogeneously broadened, the strong-coupling regime of cavity QED is typically required, which is hard to realize in actual experimental setups. Here, we show that a high-fidelity entanglement operation is possible even in the weak-coupling regime in which dampings (dephasing, spontaneous emission, and cavity leakage) overwhelm the coherent coupling between a qubit and the cavity. Our proposal enables distributed quantum information processing to be perform…
