Unambiguous quantum-state filtering

Takeoka, Masahiro; Ban, Masashi; Sasaki, Masahide

doi:10.1103/physreva.68.012307

Cited by 10 publications

(8 citation statements)

References 14 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the problem of finding the optimal unambiguous state discrimination procedure reduces to finding the values of p j that optimize the success probability 29) subject to the constraint that the 3 × 3 matrix, whose elements are…”

Section: More Than Two Pure Statesmentioning

confidence: 99%

See 1 more Smart Citation

Discrimination of quantum states

Bergou

2010

Journal of Modern Optics

209

223

View full text Add to dashboard Cite

Abstract. The problem of discriminating among given nonorthogonal quantum states is underlying many of the schemes that have been suggested for quantum communication and quantum computing. However, quantum mechanics puts severe limitations on our ability to determine the state of a quantum system. In particular, nonorthogonal states cannot be discriminated perfectly, even if they are known, and various strategies for optimum discrimination with respect to some appropriately chosen criteria have been developed. In this article we review recent theoretical progress regarding the two most important optimum discrimination strategies. We also give a detailed introduction with emphasis on the relevant concepts of the quantum theory of measurement. After a brief introduction into the field, the second chapter deals with optimum unambiguous, i. e error-free, discrimination. Ambiguous discrimination with minimum error is the subject of the third chapter. The fourth chapter is devoted to an overview of the recently emerging subfield of discriminating multiparticle states. We conclude with a brief outlook where we attempt to outline directions of research for the immediate future. IntroductionIn quantum information and quantum computing the carrier of information is some quantum system and information is encoded in its state [1]. The state, however, is not an observable in quantum mechanics [2] and, thus, a fundamental problem arises: after processing the information -i.e. after the desired transformation is performed on the input state by the quantum processor -the information has to be read out or, in other words, the state of the system has to be determined. When the possible target states are orthogonal, this is a relatively simple task if the set of possible states is known. But when the possible target states are not orthogonal they cannot be discriminated perfectly, and optimum discrimination with respect to some appropriately chosen criteria is far from being trivial even if the set of the possible nonorthogonal states is known. Thus the problem of discriminating among nonorthogonal states is ubiquitous in quantum information and quantum computing, underlying many of the communication and computing schemes that have been suggested so far. It is the purpose of this article to review various theoretical schemes that have been developed for discriminating among nonorthogonal quantum states. The corresponding experimental

show abstract

Section: More Than Two Pure Statesmentioning

confidence: 99%

“…It, too, can be recast in a form of discriminating between mixed states. The problem of filtering a mixed state out of many was addressed by Takeoka, et al in [29].…”

Section: Unambiguous Filteringmentioning

confidence: 99%

Discrimination of quantum states

Bergou

2010

Journal of Modern Optics

209

223

View full text Add to dashboard Cite

show abstract

“…For simplicity of the analysis, we consider only two outcomes: zero photons in both detectors or other events, {|0 0|⊗|0 0|, I −|0 0|⊗|0 0|} (photon number discrimination may further improve the performance but to simplify the discussion here, we leave it for a future work). Note that this mirror-image like detection strategy has been considered in the context of state 5 discrimination [18,19] and also the phase estimation via coherent-state input [20]. Since we need the phase information of the input state at the anti-squeezing process, this is a phase-sensitive measurement, and so the POVM has access to external phase information and the phase of the squeezerŜ † .…”

mentioning

confidence: 99%

Fundamental precision limit of a Mach-Zehnder interferometric sensor when one of the inputs is the vacuum

et al. 2017

Self Cite

View full text Add to dashboard Cite

In the lore of quantum metrology, one often hears (or reads) the following no-go theorem: If you put vacuum into one input port of a balanced Mach-Zehnder Interferometer, then no matter what you put into the other input port, and no matter what your detection scheme, the sensitivity can never be better than the shot noise limit (SNL). Often the proof of this theorem is cited to be in Ref. [C. Caves, Phys. Rev. D 23, 1693(1981], but upon further inspection, no such claim is made there. A quantum-Fisher-information-based argument suggestive of this no-go theorem appears in Ref. [M. Lang and C. Caves, Phys. Rev. Lett. 111, 173601 (2013)], but is not stated in its full generality. Here we thoroughly explore this no-go theorem and give the rigorous statement: the nogo theorem holds whenever the unknown phase shift is split between both arms of the interferometer, but remarkably does not hold when only one arm has the unknown phase shift. In the latter scenario, we provide an explicit measurement strategy that beats the SNL. We also point out that these two scenarios are physically different and correspond to different types of sensing applications.Introduction.-In the field of quantum metrology [1][2][3], a Mach-Zehnder interferometer (MZI) is a tried and true workhorse that has the additional advantage that any result obtained for it also applies to a Michelson interferometer (MI) and hence has a potential application to gravitational wave detection. In most current implementations of gravitational wave detectors, the MI is fed with a strong coherent state of light in one input port and vacuum in the other (Fig. 1). It was in this context that Caves in 1981 [4] showed that such a design would always only ever achieve the shotnoise limit (SNL). Then he showed if you put squeezed vacuum into the unused port, you could beat the SNL. Several implementations of this squeezed vacuum scheme have already been demonstrated in the GEO 600 gravitational detector, and plans are underway to utilize this approach in the LIGO and VIRGO detectors in the future [5,6].It then appeared, that in the lore of quantum metrology, this result was extended -without proof -to the following no-go theorem: If you put quantum vacuum into one input port of a balanced MZI, then no matter what quantum state of light you put into the other input port, and no matter what your detection scheme, the sensitivity can never be better than the SNL. Often the proof of this theorem is cited to be the original 1981 paper by Caves [4], but upon further inspection, no such general claim is made there. A quantum-Fisherinformation-based argument suggestive of this no-go theorem appeared in Ref. [7] by Lang and Caves, but it does not explore the statement in adequate generality.In this work, we give a full statement of the no-go theorem. The statement proved here is the following: if the unknown phase shifts are in both of the two arms of the MZI, then the no-go theorem holds no matter whether the MZI is balanced or not. However, in the case where the unknown phas...

show abstract

“…2 However, encoding information on multiple coherent states 3 requires the implementation of optimized strategies for their detection and discrimination, as they are non-hortogonal. 4 During the last decade, many solu-tions, based on homodyne detection, or ON/OFF or photon-number resolving detection, have been theoretically 5,6,7,8,9 and experimentally investigated. 10,11,12,13,14 The simplest setup is represented by a quasi-optimal discrimination scheme, in which the coherent states to be analyzed, namely | + α and | − α , interfere with a local oscillator (LO) |z at a high-transmissivity beam splitter (BS), whose outputs are measured by direct detection (Kennedy-like receiver 15 ).…”

Section: Introductionmentioning

confidence: 99%

Bracket states for communication protocols with coherent states

Allevi

Olivares

Bondani

2014

Int. J. Quantum Inform.

View full text Add to dashboard Cite

We present the generation and characterization of the class of bracket states, namely phase-sensitive mixtures of coherent states exhibiting symmetry properties in the phase-space de- scription. A bracket state can be seen as the statistical ensemble arriving at a receiver in a typical coherent-state-based communication channel. We show that when a bracket state is mixed at a beam splitter with a local oscillator, both the emerging beams exhibit a Fano factor larger than 1 and dependent on the relative phase between the input state and the local oscil- lator. We discuss the possibility to exploit this dependence to monitor the phase difference for the enhancement of the performances of a simple communication scheme based on direct detection. Our experimental setup involves linear optical elements and a pair of photon-number- resolving detectors operated in the mesoscopic photon-number domain

show abstract

Unambiguous quantum-state filtering

Cited by 10 publications

References 14 publications

Discrimination of quantum states

Discrimination of quantum states

Fundamental precision limit of a Mach-Zehnder interferometric sensor when one of the inputs is the vacuum

Bracket states for communication protocols with coherent states

Contact Info

Product

Resources

About