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Articles 121 - 150 of 235
Full-Text Articles in Quantum Physics
Experimental Demonstration Of Direct Path State Characterization By Strongly Measuring Weak Values In A Matter-Wave Interferometer, Tobias Denkmayr, Hermann Geppert, Hartmut Lemmel, Mordecai Waegell, Justin Dressel, Yuji Hasegawa, Stephan Sponar
Experimental Demonstration Of Direct Path State Characterization By Strongly Measuring Weak Values In A Matter-Wave Interferometer, Tobias Denkmayr, Hermann Geppert, Hartmut Lemmel, Mordecai Waegell, Justin Dressel, Yuji Hasegawa, Stephan Sponar
Mathematics, Physics, and Computer Science Faculty Articles and Research
A method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently, Vallone and Dequal [Phys. Rev. Lett. 116, 040502 (2016)] showed theoretically that weak measurements are not a necessary condition to determine the weak value. Here, we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system’s quantum state was characterized via direct measurements, using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones for tomographic accuracy. Our results are …
Janus Sequences Of Quantum Measurements And The Arrow Of Time, Andrew N. Jordan, Areeya Chantasri, Kater Murch, Justin Dressel, Alexander N. Korotkov
Janus Sequences Of Quantum Measurements And The Arrow Of Time, Andrew N. Jordan, Areeya Chantasri, Kater Murch, Justin Dressel, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the time reversal symmetry of quantum measurement sequences by introducing a forward and backward Janus sequence of measurements. If the forward sequence of measurements creates a sequence of quantum states in time, starting from an initial state and ending in a final state, then the backward sequence begins with the time-reversed final state, exactly retraces the intermediate states, and ends with the time-reversed initial state. We prove that such a sequence can always be constructed, showing that unless the measurements are ideal projections, it is impossible to tell if a given sequence of measurements is progressing forward or …
Is A Time Symmetric Interpretation Of Quantum Theory Possible Without Retrocausality?, Matthew S. Leifer, Matthew F. Pusey
Is A Time Symmetric Interpretation Of Quantum Theory Possible Without Retrocausality?, Matthew S. Leifer, Matthew F. Pusey
Mathematics, Physics, and Computer Science Faculty Articles and Research
Huw Price has proposed an argument that suggests a time-symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ-mediation, that plausibly holds independently of the status of the quantum state. We …
Saving The Physics Ii: Who Needs To Be Saved? It Depends On Your Metaphysics, Menas Kafatos
Saving The Physics Ii: Who Needs To Be Saved? It Depends On Your Metaphysics, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
Physics does not need to be saved. If anything, physics was rescued in the early twentieth century with the advancement of both the theories of relativity and quantum mechanics. What needs to be saved is our world outlook or metaphysics because how a society acts and develops depends on what its belief systems are. Here we explore how a new metaphysics where consciousness is fundamental might just be what modern societies need.
Gamifying Quantum Theory, Matthew S. Leifer
Gamifying Quantum Theory, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"Over the past few years, the trend of gamification has gradually seeped into quantum research, education and outreach, so that we now have a critical mass of games based on quantum mechanics. I thought the time was right to discuss quantum gamification at the APS March meeting[.]"
Review Of Qbism: The Future Of Quantum Physics, Matthew S. Leifer
Review Of Qbism: The Future Of Quantum Physics, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A review of QBism: The Future of Quantum Physics by Hans Christian von Baeyer.
Probing Quantumness With Joint Continuous Measurements Of Non-Commuting Observables, Luis Pedro García-Pintos, Justin Dressel
Probing Quantumness With Joint Continuous Measurements Of Non-Commuting Observables, Luis Pedro García-Pintos, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
We analyze the continuous measurement of two noncommuting observables for a qubit, and investigate whether the simultaneously observed noisy signals are consistent with the evolution of an equivalent classical system. Following the approach outlined by Leggett and Garg, we show that the readouts violate macrorealistic inequalities for arbitrarily short temporal correlations. Moreover, the derived inequalities are manifestly violated even in the absence of Hamiltonian evolution, unlike for Leggett-Garg inequalities that use a single continuous measurement. Such a violation should indicate the failure of at least one postulate of macrorealism: either physical quantities do not have well-defined values at all times …
Realisation Of Qudits In Coupled Potential Wells, Ariel Landau, Yakir Aharonov, Eliahu Cohen
Realisation Of Qudits In Coupled Potential Wells, Ariel Landau, Yakir Aharonov, Eliahu Cohen
Mathematics, Physics, and Computer Science Faculty Articles and Research
Quantum computation strongly relies on the realisation, manipulation and control of qubits. A central method for realizing qubits is by creating a double-well potential system with a significant gap between the first two eigenvalues and the rest. In this work we first revisit the theoretical grounds underlying the double-well qubit dynamics, then proceed to suggest novel extensions of these principles to a triple-well qutrit with periodic boundary conditions, followed by a general d-well analysis of qudits. These analyses are based on representations of the special unitary groups SU(d) which expose the systems' symmetry and employ them for performing computations. We …
The Quantum Universe: Philosophical Foundations And Oriental Medicine, Menas Kafatos, Keun-Hang Susan Yang
The Quantum Universe: Philosophical Foundations And Oriental Medicine, Menas Kafatos, Keun-Hang Susan Yang
Mathematics, Physics, and Computer Science Faculty Articles and Research
The existence of universal principles in both science and medicine implies that one canexplore their common applicability. Here we explore what we have learned from quantummechanics, phenomena such as entanglement and nonlocality, the role of participationof the observer, and how these may apply to oriental medicine. The universal principles ofintegrated polarity, recursion, and creative interactivity apply to all levels of existence and allhuman activities, including healing and medicine. This review examines the possibility thatwhat we have learned from quantum mechanics may provide clues to better understandthe operational principles of oriental medicine in an integrated way. Common to both isthe assertion …
Quantum Enigma Machine: Experimentally Demonstrating Quantum Data Locking, Daniel J. Lum, John C. Howell, M. S. Allman, Thomas Gerrits, Varun B. Verma, Sae Woo Nam, Cosmo Lupo, Seth Lloyd
Quantum Enigma Machine: Experimentally Demonstrating Quantum Data Locking, Daniel J. Lum, John C. Howell, M. S. Allman, Thomas Gerrits, Varun B. Verma, Sae Woo Nam, Cosmo Lupo, Seth Lloyd
Mathematics, Physics, and Computer Science Faculty Articles and Research
Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) …
Measuring A Transmon Qubit In Circuit Qed: Dressed Squeezed States, Mostafa Khezri, Eric Mlinar, Justin Dressel, A. N. Korotkov
Measuring A Transmon Qubit In Circuit Qed: Dressed Squeezed States, Mostafa Khezri, Eric Mlinar, Justin Dressel, A. N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using circuit QED, we consider the measurement of a superconducting transmon qubit via a coupled microwave resonator. For ideally dispersive coupling, ringing up the resonator produces coherent states with frequencies matched to transmon energy states. Realistic coupling is not ideally dispersive, however, so transmon-resonator energy levels hybridize into joint eigenstate ladders of the Jaynes–Cummings type. Previous work has shown that ringing up the resonator approximately respects this ladder structure to produce a coherent state in the eigenbasis (a dressed coherent state). We numerically investigate the validity of this coherent-state approximation to find two primary deviations. First, resonator ring-up leaks small …
Quantum Paradox Of Choice: More Freedom Makes Summoning A Quantum State Harder, Emily Adlam, Adrian Kent
Quantum Paradox Of Choice: More Freedom Makes Summoning A Quantum State Harder, Emily Adlam, Adrian Kent
Mathematics, Physics, and Computer Science Faculty Articles and Research
The properties of quantum information in space-time can be investigated by studying operational tasks, such as “summoning,” in which an unknown quantum state is supplied at one point and a call is made at another for it to be returned at a third. Hayden and May [arXiv:1210.0913] recently proved necessary and sufficient conditions for guaranteeing successful return of a summoned state for finite sets of call and return points when there is a guarantee of at most one summons. We prove necessary and sufficient conditions when there may be several possible summonses and complying with any one constitutes success, and …
Fundamental Awareness: A Framework For Integrating Science, Philosophy And Metaphysics, Neil D. Theise, Menas Kafatos
Fundamental Awareness: A Framework For Integrating Science, Philosophy And Metaphysics, Neil D. Theise, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
The ontologic framework of Fundamental Awareness proposed here assumes that non-dual Awareness is foundational to the universe, not arising from the interactions or structures of higher level phenomena. The framework allows comparison and integration of views from the three investigative domains concerned with understanding the nature of consciousness: science, philosophy, and metaphysics. In this framework, Awareness is the underlying reality, not reducible to anything else. Awareness and existence are the same. As such, the universe is non-material, self-organizing throughout, a holarchy of complementary, process driven, recursive interactions. The universe is both its own first observer and subject. Considering the world …
Quantum And Classical Optics–Emerging Links, Joseph H. Eberly, Xiao-Feng Qian, Asma Al Qasimi, Hazrat Ali, M. A. Alonso, R Gutiérrez-Cuevas, Bethany Little, John C. Howell, Tanya Malhotra, A. N. Vamivakas
Quantum And Classical Optics–Emerging Links, Joseph H. Eberly, Xiao-Feng Qian, Asma Al Qasimi, Hazrat Ali, M. A. Alonso, R Gutiérrez-Cuevas, Bethany Little, John C. Howell, Tanya Malhotra, A. N. Vamivakas
Mathematics, Physics, and Computer Science Faculty Articles and Research
Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of …
Nonlocality Of The Aharonov-Bohm Effect, Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Nonlocality Of The Aharonov-Bohm Effect, Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
Although the Aharonov-Bohm and related effects are familiar in solid-state and high-energy physics, the nonlocality of these effects has been questioned. Here we show that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they cannot explain the instantaneous aspect. Thus the Aharonov-Bohm effect is, in general, nonlocal.
Preserving Entanglement During Weak Measurement Demonstrated With A Violation Of The Bell–Leggett–Garg Inequality, T. C. White, J. Y. Mutus, Justin Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, John M. Martinis
Preserving Entanglement During Weak Measurement Demonstrated With A Violation Of The Bell–Leggett–Garg Inequality, T. C. White, J. Y. Mutus, Justin Dressel, J. Kelly, R. Barends, E. Jeffrey, D. Sank, A. Megrant, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, John M. Martinis
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak measurement has provided new insight into the nature of quantum measurement, by demonstrating the ability to extract average state information without fully projecting the system. For single-qubit measurements, this partial projection has been demonstrated with violations of the Leggett–Garg inequality. Here we investigate the effects of weak measurement on a maximally entangled Bell state through application of the Hybrid Bell–Leggett–Garg inequality (BLGI) on a linear chain of four transmon qubits. By correlating the results of weak ancilla measurements with subsequent projective readout, we achieve a violation of the BLGI with 27 s.d.s. of certainty.
Weak Values Are Quantum: You Can Bet On It, Alessandro Romito, Andrew N. Jordan, Yakir Aharonov, Yuval Gefen
Weak Values Are Quantum: You Can Bet On It, Alessandro Romito, Andrew N. Jordan, Yakir Aharonov, Yuval Gefen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The outcome of a weak quantum measurement conditioned to a subsequent post-selection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective measurements. However, a classical model has been recently put forward that can reproduce peculiar expectation values, reminiscent of weak values. This led the authors of that work to claim that weak values have an entirely classical explanation. Here we discuss what is quantum about weak values with the help of a simple model based on basic quantum mechanics. We first demonstrate how a classical theory can indeed …
Quantum Violation Of The Pigeonhole Principle And The Nature Of Quantum Correlations, Yakir Aharonov, Fabrizio Colombo, S. Popescu, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen
Quantum Violation Of The Pigeonhole Principle And The Nature Of Quantum Correlations, Yakir Aharonov, Fabrizio Colombo, S. Popescu, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The pigeonhole principle: "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole" is an obvious yet fundamental principle of Nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum …
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi
Mathematics, Physics, and Computer Science Faculty Articles and Research
Retrocausal models of quantum mechanics add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time arrows, such that each system can forecast future events for the other. The loop is avoided by the fact that the choice to abort an event thus forecasted leads to the destruction of the forecaster's past. Physical law therefore enables prophecy of future events only as long as this prophecy is not revealed to a free agent who can otherwise render it …
Review Of Douglas Stone, Einstein And The Quantum: The Quest Of The Valiant Swabian, Matthew S. Leifer
Review Of Douglas Stone, Einstein And The Quantum: The Quest Of The Valiant Swabian, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A book review of A. Douglas Stone's Einstein and the Quantum: The Quest of the Valiant Swabian.
Interference Energy Spectrum Of The Infinite Square Well, Mordecai Waegell, Yakir Aharonov, Taylor Lee Patti
Interference Energy Spectrum Of The Infinite Square Well, Mordecai Waegell, Yakir Aharonov, Taylor Lee Patti
Mathematics, Physics, and Computer Science Faculty Articles and Research
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of …
No Return To Classical Reality, David Jennings, Matthew S. Leifer
No Return To Classical Reality, David Jennings, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by rst granting quite …
Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell
Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how weak nonlinearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrödinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that, over any distance in this channel, the quantum bit error rate is identically zero, in principle, and …
Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov
Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
In modern circuit QED architectures, superconducting transmon qubits are measured via the state-dependent phase and amplitude shift of a microwave field leaking from a coupled resonator. Determining this shift requires integrating the field quadratures for a nonzero duration, which can permit unwanted concurrent evolution. Here we investigate such dynamical degradation of the measurement fidelity caused by a detuned neighboring qubit. We find that in realistic parameter regimes, where the qubit ensemble-dephasing rate is slower than the qubit-qubit detuning, the joint qubit-qubit eigenstates are better discriminated by measurement than the bare states. Furthermore, we show that when the resonator leaks much …
Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent
Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.
Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
Are the electromagnetic scalar and vector potentials dispensable? Vaidman [Phys. Rev. A 86, 040101(R) (2012)] has suggested that local interactions of gauge-invariant quantities, e.g., magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze six thought experiments that challenge this suggestion. All of them have explanations in terms of local interactions of gauge-dependent quantities, and, in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant formal description and that, in general, no local description can dispense with electromagnetic potentials.
Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly
Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly
Mathematics, Physics, and Computer Science Faculty Articles and Research
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger’s famous remark about it [Proc. Cambridge Philos. Soc. 31, 555 (1935)], prompts the examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments and report here values of the Bell parameter greater than ℬ=2.54. This is many standard deviations outside the limit ℬ=2 established by the Clauser–Horne–Shimony–Holt Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson …
How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov
How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Current methods for measuring magnetic flux are based on performing many measurements over a large ensemble of electrons. We propose a novel method based on wave function "revival" for measuring the flux modulo using only a single electron. A preliminary analysis of the feasibility of the experiment is provided.
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single …
Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a nonguess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and nonguess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case.We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement.Notably, while the cost advantage …