Conclusive inner product modification (original) (raw)

Quantum Time Evolution in Terms of Nonredundant Probabilities

Physical Review Letters, 2000

Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an unambiguous description of the quantal dynamics. This is shown explicitly for a single spin s, using a quorum of expectation values which contains no redundant information. The quantum mechanical time evolution of the system is rephrased in terms of a closed set of linear first-order differential equation coupling ͑2s 1 1͒ 2 expectation values. This new representation of the dynamical law refers neither to the wave function of the system nor to its statistical operator.

Physical realizations of quantum operations

Physical Review A, 2003

Quantum operations ͑QO's͒ describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO and give explicit realizations in terms of freeevolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.

Quantum state engineering via unitary transformations

Physical Review A, 1998

We construct a Hamiltonian for the generation of arbitrary pure states of the quantized electromagnetic field. The proposition is based upon the fact that a unitary transformation for the generation of number states has been already found. The general unitary transformation here obtained, would allow the use of nonlinear interactions for the production of pure states. We discuss the applicability of this method by giving examples of generation of simple superposition states. We also compare our Hamiltonian with the one resulting from the interaction of trapped ions with two laser fields. 42.50.Ct, 42.50.Dv

Estimation of unitary quantum operations

Physical Review A, 2004

The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts, and then measure the joint output state. This measurement could be an entangled one or it could be separable (e.g., measurements which can be implemented with local operations and classical comunication or LOCC). A comparison is made between these possibilities and it is shown that by using nonseparable measurements one can improve the accuracy of the estimation by a factor of 2(d + 1)/d where d is the dimension of the Hilbert space on which U acts.

Quantum and classical bounds for unknown two-state overlaps

arXiv: Quantum Physics, 2019

Suppose we have NNN quantum systems in unknown states left∣psiirightrangle\left|\psi_i \right\rangleleft∣psiirightrangle, but know the value of some pairwise overlaps left∣langlepsik∣psilrangleright∣2\left| \langle \psi_k |\psi_l\rangle \right|^2left∣langlepsik∣psilrangleright∣2. What can we say about the values of the unknown overlaps? We provide a complete answer to this problem for 3 pure states and two given overlaps, and a way to obtain bounds for the general case. We discuss how the answer contrasts from that of a classical model, and describe two applications: dimension witnesses, and characterisation of multi-photon indistinguishability.

Decoherence assisting a measurement-driven quantum evolution process

Physical Review A, 2006

We study the problem of driving an unknown initial mixed quantum state onto a known pure state without using unitary transformations. This can be achieved, in an efficient manner, with the help of sequential measurements on at least two unbiased bases. However here we found that, when the system is affected by a decoherence mechanism, only one observable is required in order to achieve the same goal. In this way the decoherence can assist the process. We show that, depending on the sort of decoherence, the process can converge faster or slower than the method implemented by means of two complementary observables. PACS numbers: 03.67.-a, 03.65.-w

Orthogonalization of partly unknown quantum states

Physical Review A, 2014

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 of under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalization of partly unknown single-and two-qubit quantum states. A state orthogonal to an input state is conditionally prepared by quantum filtering, and the only required information about the input state is a mean value of a single arbitrary operator. We show that perfect orthogonalization of partly unknown two-qubit entangled states can be performed by applying the quantum filter to one of the qubits only.

Subsystem measurement in unitary quantum measurement theory with redundant entanglement

Measurement of a degenerate (or non-degenerate) discrete observable is investigated in the framework of quantum measurement theory short of collapse, i.e. premeasurement theory, based on a unitary evolution operator that includes the measurement interaction between object and measuring instrument. A pointer observable with eigen-projectors of, in general, many (or even in¯nitely) dimensional ranges is introduced as a new approach. It leads to redundant entanglement in the¯nal state. As the¯rst main result, the basic dynamical relation of the approach is derived. It is shown to be equivalent to the calibration condition, which is known to de¯ne general exact measurement. The latter is given a practical form. Complete measurement (premeasurement with objecti¯cation or collapse), which is in some sense implied by the premeasurement theory, performed on a subsystem of a bipartite object in a pure state is studied with particular attention to its e®ect on the opposite, interactionally una®ected subsystem. The change of state of the latter is derived for exact complete subsystem measurement, and it is shown that the change is the same as for the simplest, i.e. ideal measurement (this is the second main result). It is applied to the case of twin observables and thus distant measurement obtains a new, more satisfactory, foundation (the third main result). Distant measurement is a basic concept in the EPR phenomenon. The well-known importance of the latter implies importance of the former.

On state vs. channel quantum extension problems: exact results for UxUxU symmetry

We develop a framework which unifies seemingly different extension (or "joinability") problems for bipartite quantum states and channels. This includes well known extension problems such as optimal quantum cloning and quantum marginal problems as special instances. Central to our generalization is a variant of the Choi-Jamiolkowski isomorphism between bipartite states and dynamical maps which we term the "homocorrelation map": while the former emphasizes the preservation of the positivity constraint, the latter is designed to preserve statistical correlations, allowing direct contact with entanglement. In particular, we define and analyze state-joining, channel-joining, and local-positive joining problems in three-party settings exhibiting collective U ⊗ U ⊗ U symmetry, obtaining exact analytical characterizations in low dimension. Suggestively, we find that bipartite quantum states are limited in the degree to which their measurement outcomes may agree, while quantum channels are limited in the degree to which their measurement outcomes may disagree. Loosely speaking, quantum mechanics enforces an upper bound on the extent of positive correlation across a bipartite system at a given time, as well as on the extent of negative correlation between the state of a same system across two instants of time. We argue that these general statistical bounds inform the quantum joinability limitations, and show that they are in fact sufficient for the three-party U ⊗ U ⊗ U -invariant setting.

Manipulations Between Eigenstates of 2-Level Quantum System Based on Optimal Measurements

This paper explores the manipulation between eigenstates in a two-level system by a sequence of instantaneous projective measurements. Three cases of the manipulations are studied: the manipulation of optimal measurement-based control; the optimal measurement-based manipulation with the effect of free evolution of system; and the external control fields being used to compensate for the effect caused by the free evolution. Numerical simulations are conducted to verify the results obtained from the theoretically analytical solutions. The optimal parameters for each manipulation case are obtained. The experimental results indicate that the external control fields can make the optimal measurement-based control more effective. Citation: Jingbei Yang, Shuang Cong, Feng Shuang, Herschel Rabitz. Manipulations between eigenstates of 2-level quantum system based on optimal measurements. IEEE/CAA Journal of Automatica Sinica, 2016, 3(1): 35-41