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arXiv:1205.3877 · Physical Review Letters

Null Values and Quantum State Discrìmination

Oded Zilberberg, Alessandro Romito, David J. Starling, Gregory A. Howland, Curtis J. Broadbent, John C. Howell, Yuval Gefen

Published Apr 25, 2013• 26 citations
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Abstract

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

DOI
10.1103/physrevlett.110.170405

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We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.
A two-step measurement protocol of a quantum system, known as weak value (WV), has been introduced more than two decades ago by Aharonov et al. [1], and has since been studied in various contexts. Here we discuss another two-step measurement protocol which we dub null weak value (NWV). The protocol consists of a partial-collapse measurement followed by quantum manipulation on the system and finally a strong measurement. The first step is a strong measurement which takes place with small probability. The second strong measurement is used as postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a non-trivial correlation between the two measurements. The NVW protocol, first defined for a two-level system [2], is generalized to a multi-level system, and compared to the standard-WV protocol.
A two-step measurement protocol of a quantum system, known as the weak value (WV), was introduced more than two decades ago by Aharonov et al (1988 Phys. Rev. Lett. 60 1351) and has since then been studied in various contexts. In this paper, we discuss another two-step measurement protocol that we dub the null weak value (NWV). The protocol consists of a partial-collapse measurement followed by quantum manipulation on the system and finally a strong measurement. The first step is a strong measurement which takes place with a small probability. The second strong measurement is used as a postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a nontrivial correlation between the two measurements. The NVW protocol, first defined for a two-level system (Zilberberg et al 2012 arXiv:1205.3877), is then generalized to a multi-level system and compared with the standard-WV protocol.
We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states $\ensuremath{\mid}{\ensuremath{\Psi}}_{0}⟩$ and $\ensuremath{\mid}{\ensuremath{\Psi}}_{1}⟩$. We distribute the qubits to two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability that would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit, and qudit, states. Applications to quantum secret sharing are discussed. Finally, we present an optical scheme to experimentally realize the protocol in the case of two qubits.
Abstract We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate information. The success statistics of the task provides an upper bound for the amount of incompatibility of the two measurements, as it is quantified by means of their incompatibility robustness. For a broad class of unbiased and possibly noisy qubit measurements, one can make this upper bound coincide with the true value of the robustness by suitably tuning the preparation of the experiment. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons’ polarization degrees of freedom, and incompatibility is directly accessed by virtue of a refined control on the amplitude, phase and purity of the final projection stage of the measurements. Our work thus establishes the practical feasibility of a recently proposed method for the detection of quantum incompatibility.
Abstract The discrimination of quantum measurements is an important aspect of quantum information processes. In this paper we present a novel protocol for local quantum measurement discrimination (LQMD) via selective projective measurements with numerous multi-qubit GHz entangled states. In this protocol, we assume that there is no classical channel between two space-like separated parties (Alice and Bob). To ensure that their operations proceed in an orderly fashion they agree that Alice measures her qubits before a specified time while Bob measures his after this time. Furthermore, a method for comparing measurement results is employed, that is, after Alice’s measurement, Bob does not calculate the reduced density matrix of his system but compares the probability of all his qubits being in states | 0 ⟩ or | 1 ⟩ after measuring his qubits under the basis { | 0 ⟩ , | 1 ⟩ } . It is shown that after this the local discrimination of two different kinds of measurement can be completed via numerous eight-qubit GHz entangled states and selective projective measurements without the help of classical information. This means that that no-signaling constraint can be violated by LQMD.
We quantify the disturbance of a quantum state undergoing a sequence of observations and particularly focus on a weak measurement followed by postselection and compare these results to the projective counterpart. Taking into account the distinguishability of both the system and the device, we obtain the exact trade-off between the system state disturbance and the change in the device pointer state. We show that for particular postselection procedures the coupling strength between the system and the device can be significantly reduced without losing measurement sensitivity, which is directly transferred to a reduced state disturbance of the system. We observe that a weak measurement alone does not provide this advantage, and only in combination with postselection is a significant improvement in terms of increased measurement sensitivity and reduced state disturbance found. We further show that under realistic experimental conditions this state disturbance is small, whereas the exact postselection probability is considerably larger than the approximate value given by the overlap of the initial and final states when neglecting the system state disturbance.